Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 There are different methods we use to calculate square roots of a given number. Some of the methods we use are given below:

2 Prime Factorization Method:

3 While using the<a></a><a>prime factorization</a>method for square root calculation, a number is represented as the product of its prime<a>factors</a>. Remember that this method is only applicable to perfect square numbers. To find the square root of a perfect square, the prime factorization is the most commonly used method. We need to follow the steps mentioned below to calculate the square root of a number:

4 Step 1:Break down a number into its prime factors. Start with the smallest<a>prime number</a>, which is 2.

5 Step 2:Group pairs of factors, where both factors in each pair are the same.

6 Step 3:Take one factor from each pair.

7 Step 4:Multiply the factors. The square root of a given number is the product of their factors.

8 For instance, take a look at this example of the square root of 144:

9 \(144 = 2 × 2 × 2 × 2 × 3 × 3\)

10 \((2 × 2) × (2 × 2) × (3 × 3)\)

11 \((2 × 2 × 3)\)

12 \(144 = 122\)

13 \(√144 = 12\)

14 The square root of 144 is \( ±12\).

15 Long Division Method:

16 To find the square root of an imperfect number, we can apply the long<a></a><a>division</a>method. In this method, large numbers will be broken down into small parts. The several steps of this method are:

17 Step 1:Break a number into pairs of two digits from right to left.

18 Step 2:Find the greatest number whose square is smaller or equal to the first digit or pair.

19 Step 3:Now we can subtract the square of that number from the pair. After that, we can drop the next pair of numbers.

20 Step 4:Double the number you found in step 2, and you get the new<a>divisor</a>.

21 Step 5:When we reach the required level, we can stop the steps.

22 For example, we can find the square root of 20:

23 Step 1:We have one pair of digits for 20.

24 Step 2:4 is the largest number whose square is smaller than or equal to 20, because \((4 × 4 = 16)\). The first digit of the square root of 20 is ±4.

25 Step 3:Subtract 16 from 20. \(20 - 16 = 4\)

26 Now, we have to drag down the next pair. But here, there is no other pair. So add a zero and make it 400.

27 Step 4:Double the digit 4 and we get 8 as the result.

28 Step 5:Next, we find the largest number, whose square is<a>less than</a>or equal to 400, when we multiply by the new number and add to 8. Here, 5 is the next digit. \(8 × 5 = 40\) \(40 × 5 = 200\)

29 Step 6:Subtract 200 from 400 which gives 200. Now, we know the approximate square root of 20 is ±4.5.

30 Using a Calculator:

31 This is a simple and interesting way to calculate the square roots of any given number. Finding the<a>symbol</a>of square root √ in the<a>calculator</a>is the foremost thing you should remember. Just enter your number, then press the square root symbol √. The calculator will display the square root.