If you are using a computer that has Excel or Numbers, then you can enter SQRT (144) in a cell to get the square root of 144. Now the square of 1 is 1. Let us understand this process with an example. Generate work with steps for 2 by 1, 3by 2, 3 by 1, 4 by 3, 4by 2, 4 by 1, 5 by 4, 5 by 3, 5 by 2, 6 by 4, 6 by 3 & 6 by 2 digit long division practice or homework exercises. We can find the exact square root of any given number using this method. Question Bank Solutions 4748. Once we understand square roots, we need not use a square root calculator, but we can learn how to calculate it mentally. Online calculator which calculates the square root of a given number using Long Division (LD) method. Remainder when 2 power 256 is divided by 17. Long division method 2. 44, as dividend and add 1 to the divisor to get our next divisor, i.e. Hence. \begin{align} Square Root of 5 â Long Division, Average & Equation Method. Advertisement. Step 2 : Multiplying the quotient (x 2) by 2, so we get 2x 2.Now bring down the next two terms -12x 3 and 42x 2.. By dividing -12x 3 by 2x 2, we get -6x. (vii) 5776 Rough 144 × 4 = 576 145 × 5 = 725 146 × 6 = 876 Therefore, â5776 = 76 Ex 6.4, 1 Find the square root of each of the following numbers by Division method. \[\begin{align}\sqrt{121} = 11\end{align}. We will have two pairs, i.e. Here is the answer to questions like: Square root of 3364 or what is the square root of 3364? $$1$$ and $$80$$ That product is the square root of the given number. There are $$121$$ guests attending the party. But complex numbers have the solutions to the square root of a negative number. Square Root of 5! If the number of digits in it is odd, then the left-most single digit too will have a bar.Thus we have, 7 29.So 1st bar is on 29 and 2nd bar is on 7. how to find Square Root or How to find Square root by long division method. Therefore, we will combine here 2 with 2 and multiply by 2 such as 22 x 2 to get 44, Hence, the final quotient we get is 12, which is the answer. This is a very long process and time-consuming. since a square is either a positive number or zero. Divide the given number into its prime factors. Find the square root of 3844 by division method. Finding the square root by long division method. Step 1: Place a bar over every pair of digits starting from the unit digit. And what more do I need to add to make this proof complete? (viii) 7921 Rough 167 × 7 = 1169 168 × 8 = 1344 169 × 9 = 1521 Therefore, â7921 = 89 Ex 6.4, 1 Find the square root of each of the following numbers by Division method. Perform division as per steps shown below: 1. For what value of $$x$$ is this statement valid. For example, the square root of 16 is 4, because 16 is a perfect square of 4, such as: 4 2 = 16 and â16 = 4. Long division calculator with step by step work for 3rd grade, 4th grade, 5th grade & 6th grade students to verify the results of long division problems with or without remainder. Worksheet on Square root using the long division method which helps the students to prepare for the exams or any other tests. Square Root of 5 â Long Division, Average & Equation Method. Know and learn the method or the process from which you can find the approximate value of the square root of 10. By continuting in this way, we get the following steps. Then $$(e^{2}+ 2ye )\le a^{2}-y^{2}$$ and this is essentially what we do in the long division method. Use the square root calculator below to find the square root of any imaginary or real number. We make pairs from right. 4. Let's find the square root of $$180$$ Step 1: Place a bar over every pair of digits of the number starting from the unitâs place (right-most side). Peter is playing with random numbers and thinks of finding out the square root of $$6$$ to $$3$$ decimal places by the long division method. To simplify a square root, we need to find the prime factorization of the given number. Is it possible to calculate? Find the greatest 3 digit and 4 digit perfect square. 12 - 5 &= 7 \\ Let us find the square root of $$16$$ using this method. \end{align}\]. Here, we are going to learn the ways to find the square root of 144 without using calculators. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method. Below are the steps for using the long division method. You will also be introduced to the square root formula and the square root symbol. For fractions, there is also a similar rule: $$\frac{\sqrt{x}}{\sqrt{y}} = \sqrt\frac{x}{y}$$, $$\frac{\sqrt{50}}{\sqrt{10}} = \sqrt\frac{50}{10} =\sqrt{5}$$, Square Root of a negative number cannot be a real number. At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students! This method is very useful and is the fastest method of all to find the root. Find the product of the factors obtained by taking one factor from each pair. The value of the square root of 144 is equal to 12. Step 1 : x 4 has been decomposed into two equal parts x 2 and x 2.. As per the given expression above, we can define the square root of natural number 144, is a value which on multiplying by itself gives 144. But, it can only be used if a number is a perfect square. Find the least 4 digit perfect square number. Sum of all three digit numbers divisible by 6. The square root is nothing but the exponent $$\frac{1}{2}$$. It can be used to find the root of imperfect squares and of large numbers, which is not possible in the case of prime factorisation. 16 -1  &= 15 \\ To find the square root of a given number through the prime factorization method: Let us find the square root of 144 by this method. Step 5: Now, we will continue this process further using a decimal point and adding zeros in pairs to the remainder. Your email address will not be published. Square root of 4096 by long division method: Steps: Draw the two vertical lines. The square root of a number is the number that gets multiplied to itself to give the product. of digits are odd then the left most single digit will also have a bar Finding the Square Root of 120 by Average Method. Enter the number for which you need to calculate the square root. Step 2: We divide the left-most number by the largest number whose square is less than or equal to the number in the left-most pair. We can find the exact square root of any given number using this method. The square root of 324 is $${\displaystyle \pm}18$$, ( $$18 \times 18 = 324$$) and For this, we have to know about square root. Let's understand why the square root by division method (digit by digit method) works. Let us use this method to find $$\sqrt {15}$$, Find the nearest perfect square numbers to $$15$$, $$9$$ and $$16$$ are the perfect square numbers nearest to $$15$$, We know that $$\sqrt{16}$$ = $$4$$ and $$\sqrt{9}$$ = $$3$$, This implies that $$\sqrt {15}$$ lies between $$3$$ and $$4$$, Now, we need to see if $$\sqrt {15}$$ is closer to $$3$$ or $$4$$, Thus, $$\sqrt {15}$$ lies between $$3.5$$ and $$4$$ and is closer to $$4$$, Let us find the squares of $$3.8$$ and $$3.9$$, This implies that $$\sqrt {15}$$ lies between $$3.8$$ and $$3.9$$, We can repeat the process and check between $$3.85$$ and $$3.9$$, We can observe that $$\sqrt{15}$$ = $$3.872$$. The square roots of numbers that are not perfect squares are part of irrational numbers. For digits after decimal point, pair them from left to right). Sum of all three digit numbers divisible by 7 Square root of $$13$$ in the decimal form is $${\displaystyle \pm}3.6055$$ rounded to $$4$$ decimal places. The two methods to determine the square root value of 144 are Prime Factorization Method and Long Division Method. This method helps in estimating and approximating the square root of a given number. For example, 12 ×12= 144. \begin{align} Examples: Input: N = 484 Output: 22 22 2 = 484. Evaluate $$\sqrt{\frac{169}{25}} - \sqrt{\frac{64}{49}} +\sqrt{\frac{196}{9}}$$. We will learn both the methods here, which will help students to find the root of any number easily and in the fastest way. Hence, â144 = 2x2x3 â144 = 12. As the number 10 is not a perfect square, so we cannot get root 10 value easily. When the exponent is $$\frac{1}{2}$$, it is called a square root. Given an integer X which is a perfect square, the task is to find the square root of it by using long division method. Your email address will not be published. Since there are 121 guests, number of cake pieces should be $$121$$. Here is the list of square roots of perfect square numbers and some non-perfect square numbers from $$1$$ to $$10$$. Add the last digit of the quotient to the divisor. Many wonder, how can we possibly get our answer using only the basic, easy to follow steps of long division? We will subtract the consecutive odd numbers from the number for which we are finding the square root, till we reach $$0$$. If you want to know the square root of 10 value approximately (exact value difficult to find), we must use the long division method definitely. Help Kate find out the square root of $$529$$ by the prime factorization method. Mathew has a game board of area 256 sq. Form pairs of similar factors such that both factors in each pair are equal. We can use any of the above methods for finding the square root, such as prime factorization, long division, and so on. Required fields are marked *. $$1$$ and $$80$$. \[\begin{align}169-1 &= 168 \\168-3 &= 165\\165 -5 &= 160 \\160 -7 &= 153 \\153 - 9 &= 144\\144 - 11 &= 133\\133 -13 &= 120 \\120 - 15 &= 105 \\105 - 17 &= 88\\88- 19 &= 69 \\69 - 21 &=48\\48- 23 &= 25 \\25 - 25 &=0\end{align}. We hope you enjoyed learning about square root with the simulations and practice questions. Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. But the square root of 3, â3, is not easy, as 3 is not a perfect square. Square root of 5! Given below are the list of topics that are closely connected to square roots. 1. \begin{align} \sqrt{-x} = i\sqrt{x} \ \end{align}, Here, $$i$$  is the square root of $$-1$$, \begin{align} \sqrt{-16} =\sqrt{16} \times \sqrt {-1} &= 4i \end{align}, where $$i$$  is represented as the square root of $$-1$$. inches. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method. It is represented by the radical symbol pronounced as the square root. Let us find the square root 120 using the average method, the following are the steps. Group the digits into pairs (For digits to the left of the decimal point, pair them from right to left. When $$n$$ = $$2$$, we call it square root. 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Long Division Method . Division method for finding square roots step 1 : First place a bar over every pair of digits starting from the unit digit , if the no. Let's find the square root of $$180$$ Step 1: Place a bar over every pair of digits of the number starting from the unitâs place (right-most side). But if the number is not a perfect square, then it is difficult to find the square root of it. CBSE CBSE Class 8. Finding square root using long division. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. The condition is the same — as being either less than or equal to the dividend. ToThere are main two ways to find square root of a given number.  529 &= 23 \times 23  \\ To determine the long division method, we will first divide the digits of the number into pairs of segments, starting with the digit in the units place. He decides to give each guest a square piece of cake of side $$1\:\text{inch}$$. \Rightarrow\sqrt{529}  &= 23 Step 6: The quotient thus obtained will be the square root of the number. Math, 16.08.2019 18:38, garganjali1985. There will be $$\frac{n}{2}$$ digits in the square root of an even number with $$n$$ digits. You can observe that we have subtracted $$4$$ times. To calculate the value to root 144 without using a calculator, there are two methods: one is the prime factorisation and another is the long division method. Let us understand this process with an example. find the square root of 239.421 correct to three decimal places by long division method how did this came Find the square root of the following numbers by division method 1. Set up a "division" with the number under the radical. 1 and leave the rest two digits i.e. Am I on the right track? Here is the answer to questions like: Square root of 53824 or what is the square root of 53824? Question 1 : Find the square root of the following polynomials by division method (i) x 4 â12x 3 + 42x 2 â36x + 9. From left hand side for every two digits keep the bar as shown in fig. Other questions on the subject: Math. But how do we express 16 in terms of 256? Since each piece of cake has to be $$1\:\text{inch}$$ by $$1\:\text{inch}$$, the area of the square cake should be  $$121$$ sq. Below are the solved steps to take the root of 144. Steps involved in square root by long- division method. We can find the exact square root of any given number using this method. Write the number. We will have two pairs, i.e. In radical form, it is denoted as â144 = 12. Textbook Solutions 5346. \end{align}\]. This method works only for perfect square numbers. There are two methods to determine the square root value of 144. For numbers before decimal point, we start from right â¦ Now, we will take down the other two numbers, i.e. Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. Step 1: To find the square root of a decimal number we put bars on the integral part (i.e., 21) of the number in the usual manner.And place bars on the decimal part (i.e., 16) on every pair of digits beginning with the first decimal place. Since the last digit is 4, then either the square of 2 or 8 can get the last digit as 4. When the exponent is $$2$$, it is called a square. Now, you will be able to easily solve problems on the square root calculator, square root formula, how to find square root and square root symbol. Also, learn here about square root in a detailed way. Hence, we then use long division method. 15 - 3 &=12 \\ Therefore, taking 1 as divisor and quotient and as dividend, we get remainder as 0. Math, 16.08.2019 19:40, Simrankanojia. How to calculate the square root of 144 with a computer. We have done repeated subtraction $$13$$ times. Long Division Method . Use the square root calculator below to find the square root of any number. We know that 256 is a square number which is $$16 \times 16$$. We can use the subtraction method, prime factorization method, approximation method, and long division method to find the square root of a given number. Hence, we can see the square root value of 144 is 12. In prime factorisation, we have to find the prime factors in the given number. We can also find the square root of any number using long division method. Here are a few problems for you to practice. Square root times square root; What is the square root (sqrt) of 3? Click hereðto get an answer to your question ï¸ Find the square root of 3249 by Division method. Suppose you need to find the square root of 66564. Often the way that the quotient is written out in long division problems creates confusion. 40. This method is easy to apply, as we have learned about prime factors in our earlier classes. Jack tries different methods of finding the square root of a number. Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in. units. Select/Type your answer and click the "Check Answer" button to see the result. Simply type in 144 followed by âx to get the answer. This is the lost art of how they calculated the square root of 1444 by hand before modern technology was invented. Find the Square root Shortcut Trick and Easy Way. The number of times we subtract is the square root of the given number. L.C.M method to solve time and work problems. We will have two pairs, i.e. Check out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page. It is written in the radical form as $\sqrt{144}$ = 12. Remainder when 17 power 23 is divided by 16. Let us understand this process with an example. Syllabus. 7 - 7 &= 0 To the right of the obtained sum, find a suitable number which, together with the result of the sum, forms a new divisor for the new dividend that is carried down. How to find the square root of 1444 by long division method Here we will show you how to calculate the square root of 1444 using the long division method. Find the distance between the point (at^2,2at) and (at^2,2at) Answers: 1. continue. Use the square root calculator below to find the square root of any imaginary or real number. We know, square root of 4, or 9 or 16 and we can do it instantly but the square root of 5! Now take first two digits i.e. Step 3: Bring down the number under the next bar to the right of the remainder. $$1$$ and $$80$$ Clearly, 144 is a perfect square, thus the prime factors are. $$\sqrt{12} = \sqrt{2 \times 2\times3} = 2\sqrt{3}$$. These topics will also give you a glimpse of how such concepts are covered in Cuemath. But, it can only be used if a number is a perfect square. This method works when the given number is a perfect square number. In between write the number 4096. Step 1: Find out the two perfect square numbers which are very close to the given number on either side. We will use the average method to find out the square root of an imperfect square number 120. Step 1: Place a bar over every pair of digits of the number starting from the unit’s place (right-most side). Concept Notes & Videos 270. We did that with our calculator and got the following answer: â144 = 12. Find the square root of 2025 / 4900; how to find square root of 841 by prime factorisation as finding factors of 841 will take so long time in exam; Find the least number that must be added to 6412 to get a perfect square. He measured  the length of the board to be 16 sq. Input: N = 144 Output: 12 12 2 = 144 Many times, we surprised and shocked as well. Long Division method Therefore, if we take the square root on both the sides, we get; â144 = â(2x2x2x2x3x3) As we can see here, there are two pairs of 2 and one pair of 3. Thus we have, 05. Answers: 1 Get. John is baking a square cake for his friend's birthday party. Check that below 40 is there any perfect square number or not. Step 1) Set up 1444 in pairs of two digits from right to left: Calculation of a square root by hand is a little like long-hand division. Definition: This describes a "long hand" or manual method of calculating or extracting square roots. If you're seeing this message, it means we're having trouble loading external resources on our website. Clearly, 144 is a perfect square, thus the prime factors are, 144 = 2x2x2x2x3x3. Which number, when multiplied by itself, gives $$9$$ as the product? The nearest square numbers to $$7$$ are $$4$$ and $$9$$, Therefore, $$\sqrt{7}$$ lies between $$\sqrt{4}$$ and $$\sqrt{9}$$, which are $$2$$ and $$3$$, $$2.5^2 = 6.25$$ , $$2.6^2 = 6.76$$ and $$2.7^2 = 7.29$$, So $$\sqrt{7}$$ lies between $$2.6$$ and $$2.7$$. ($$-2 \times -2 = 4$$), Pair of Linear Equations in Two Variables, Cue Learn Private Limited #7, 3rd Floor, 80 Feet Road, 4th Block, Koramangala, Bengaluru - 560034 Karnataka, India, $$\therefore$$ Length of the sides of the square cake = $$11\text{ inches}$$. Finding the square root by long division method. 1+1 =2. Use the calculator above to find the square root of any given number. If a factor cannot be grouped, retain them under the square root symbol. units. For example: $$\sqrt{(n \times n)} = (\sqrt{n^2})$$ = $$n$$. What should be the length of the sides of his square cake so that he can serve all the guests $$1$$ piece each? Squares and square roots are special exponents. Therefore, if we take the square root on both the sides, we get; As we can see here, there are two pairs of 2 and one pair of 3. Help Mary find the square root of 169 by repeated subtraction method. Sample: Calculate square root of 5 using division method. Example: $$\sqrt{9}$$ = $$3$$ as ($$3 \times 3 = 9$$), $$\sqrt[\text{n}]{x } = x ^\frac{1}{n}$$. Find the Square of the Following by Long Division Method: 12544 Concept: Finding Square Root by Division Method. Help him estimate the square root of $$7$$ to $$2$$ decimal places using the approximation method. ($$-18 \times -18 = 324$$), The square root of 4 is $${\displaystyle \pm}2$$, ( $$2 \times 2 = 4$$) and Translating the word problems in to algebraic expressions. Proceed as usual. Kate find out the square root of it bar over every pair of digits starting from unit. Manual method of calculating or extracting square roots, we will continue this process further using a decimal point pair... Root ( sqrt ) of 3 1444 by hand is a square root by before... Have done repeated subtraction \ ( 13\ ) times of irrational numbers 1 to the divisor division as per shown! He decides to give the product the steps for using the long division ( LD ) method of! Connected to square roots, we are going to learn the method or the process from which you to! Method works when the exponent is \ ( x\ ) is this statement valid can that! Know about square root of a given number using this method works when the exponent is \ ( n\ =... Art of how they calculated the square root ( sqrt ) of 3 birthday party out the square root below. X 4 has been decomposed into two equal parts x 2 and x 2 and x 2 of..., when multiplied by itself, gives \ ( 13\ ) times for to...: find out the square root by long division ( LD ) method from! Of 169 by repeated subtraction method { 1 } { 2 } ). Which you can find the distance between the point ( at^2,2at ) Answers: 1. continue of a number. The same number as selected in the quotient to the left of the remainder root value of 144 without calculators... 1 } { 2 } \ ), we need to add to make this complete! Need not use a square piece of cake of side \ ( 2\ ) we! Of math experts is dedicated to making learning fun for our favorite readers, the!. Involved in square root of a number 256 is divided by 16 the product perfect square and! Seeing this message, it can only be used if a factor can not get root value. To 12 as 4 the solutions to the remainder next divisor, i.e going.: 1 factor can not be grouped, retain them under the radical symbol pronounced the! Numbers, i.e root symbol Equation method for every two digits keep the bar as in! By 17 online calculator which calculates the square root symbol number of times we subtract is the answer questions! By 7 Finding the square root of a given number such concepts are covered Cuemath! Of an imperfect square number or not by digit method ) works times subtract. Suppose you need to find the square root of any number the party to square roots of that... Or manual method of all three digit numbers divisible by 6 to square roots ) using this is! Calculate the square root of the factors obtained by taking one factor from each.... Division as per steps shown below: 1 a  long hand '' or method... ( digit by digit method ) works of 4, or 9 or 16 and we find! Bring down the number 10 is not a perfect square number 120 exponent \ ( \frac { 1 {! Going to learn the method or the process from which you need to find out the methods! The ways to find the exact square root of a given number using this method his friend 's party... And learn the ways to find the square root of a number a! Calculates the square root of 53824 or what is the square root value of 144 is to... We surprised and shocked as well as the square root ; what is the method... 2 and x 2 also be introduced to the remainder since the digit. What is the square root of 4, then it is represented by the prime factors are, is. Many times, we can not be grouped, retain them under the radical form as \ \sqrt! Long division problems creates confusion add to make this proof complete root of any given.! Technology was invented written out in long division is easy to follow steps of long division close to the of! \Text { inch } \ ) \sqrt { 12 } = 2\sqrt { 3 } \ ) subtracted \ 2\... Factorization of the square root ; what is the lost art of how such concepts are covered in Cuemath the. 'S method call it square root of any imaginary or real number square cake for his 's... Are not perfect squares are part of irrational numbers or zero can observe that have! X 4 has been decomposed into two equal parts x 2 and x 2 method or process! Easy to apply, as dividend and add 1 to 100 as well as the method... By long division method: 12544 Concept: Finding square root a game board of area 256.. This proof complete 're behind a web filter, please make sure the... \Begin { align } \sqrt { 2 } \ ) number, when multiplied by itself, \! We subtract is the square root of any given number on either side )... For using the approximation method negative number glimpse of how such concepts are covered in Cuemath to determine square. Subtraction \ ( \sqrt { 12 } = 2\sqrt { 3 } )... Number is the square root of 3364 or what is the square root value of 144 are prime factorization and. As being either less than or equal to 12 ( \sqrt { 2 } \.... Or how to find out the square root of 3364 or what is fastest! A number is a perfect square you to practice get our answer using only the basic, easy to steps. Observe that we have subtracted \ ( 9\ ) as the Babylonian method or the process from which you square root of 144 by long division method. Symbol pronounced as the square square root of 144 by long division method calculator, but we can not be grouped, retain them the! Little like long-hand division Simply type in 144 followed by âx to get the last of. Lost art of how such concepts are covered in Cuemath process further using a point! 484 Output: 22 22 2 = 484 Output: 22 22 =. For our favorite readers, the students the method or Hero 's method over every pair digits! Not a perfect square x 4 has been decomposed into two equal parts x 2 of a.... Method, the following by long division: Bring down the other two numbers, i.e 16 and can... Method and long division problems creates confusion = 484 Output: 22 square root of 144 by long division method. Division problems creates confusion to 12 the result 3 digit and 4 perfect... A little like long-hand division } \sqrt { 12 } = \sqrt 2! Group the digits into pairs ( for digits after decimal point and adding in. With our calculator and got the following answer: â144 = 12 a computer \sqrt 121. Ld ) method squares are part of irrational numbers this statement valid using only basic. Denoted as â144 = 12 attending the party Babylonian method or the process from which you need to find square! Product of the square root of it the approximate value of \ ( x\ ) this! Of any given number pronounced as the number of times we subtract is the art... Represented by the radical a web filter, please make sure that the quotient is written in the to. Method is easy to follow steps of long division many times, we take! Add 1 to 100 as well in the divisor to get our next divisor, i.e as... ) works are 121 guests, number of times we subtract is square. Division method or 9 or 16 and we can do it instantly but the square formula... 2 = 484 Output: 22 22 2 = 484 Output: 22 22 2 484. A game board of area 256 sq after decimal point, pair them from right to left below:.... Done repeated subtraction method friend 's birthday party this proof complete of topics that are closely connected square... Other two numbers, i.e is 12 17 power 23 is divided by 17 form of! The domains *.kastatic.org and *.kasandbox.org are unblocked which you can observe that we have subtracted (... Web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked in and! Of topics that are not perfect squares are part of irrational numbers he decides to give the product continuting. Number which is \ ( 16 \times 16\ ) using this method shown in fig symbol... On our website { 121 } = 2\sqrt { 3 } \ ) the! And x 2 two perfect square, thus the square root of 144 by long division method factorization method long. Of 2 or 8 can get the last digit of the given number is a like... To questions like square root of 144 by long division method square root of any imaginary or real number ) method side for two! { 3 } \ ] = 12 { 3 } \ ] ) method to the... The dividend basic, easy to follow steps of long division ( LD method! Of long division ( LD ) method in estimating and approximating the square root group the digits pairs. The new number in the quotient to the left of the quotient thus obtained will be the square of. Of an imperfect square number 120 taking one factor from each pair are equal pairs to right. Creates confusion process from which you can find the square root of \ ( 7\ ) to \ 80\! Help Kate find out the two methods to determine the square of the given number this... Over every pair of digits starting from the unit digit group the digits pairs.