**To find the square root of a perfect square number:**

** We find the first figure by looking at the first figures and we find two possible last figures by looking at the last figure. **
** We find the first figure by looking at the first figures.**
** we find two possible last figures by looking at the last figure.**
** ****We then decide which is correct either by considering the*** digit sums* or by considering the square of their mean.

Consider for example:

1.) Square root of 12544

a. We divide the given number into two groups as 125 & 44.

b. Now we will find the nearest square number to the first group (i.e 125)

We have 11 & 12

11^2 = 121 & 12^2 = 144

Now, we need to choose between these two.

Choose the smallest value (i.e below 125) = 121

The square root of 121 = 11. This forms the first part of our answer.

c. As the second group ends with 44, therefore the square root of number ends with either 2 or 8 ( Since 2^2 = 4 & 8^2 = 64).

Here also, we have two answers. We need to find the correct answer.

We will use the** digital sum concept, **then digital sum of 112^2 = (1+1+2)^2

= 4^2 = 16 = 7. Similarly, 118^2 = (1+1+8)^2 = 1^2 =1.

12544 = ( 1+2+5+4+4) = 16=7

By observing the above two digital sum with that of given number whose square root is to be found.

Therefore, square root of 12544 = 112

2. Square root of 5929

a. Grouping will be 59 & 29.

b. Nearest square number to the first group (i.e 59)

We have 7 & 8

We will choose the first one, (i.e 7) since 7^2 = 49 is less than 59.

c. 2nd group (i.e 29), we will have two choices- 3 & 7

Now the answers are 73 &77

We need to choose one answer between above answers.

DS( 5929) = 5+9+2+9 = 7

DS(73)^2 = 1^2 =1

DS(77)^2 = 14^2 =5^2 =7

Now, comparing the above digital sum(DS). We will come know that 77 is the correct answer.

Therefore, square root of 5929 = 77

**Exercise: **

**Find the square root of**

a.) 17161

b.) 4761

c.) 53361

d.) 4356

e.) 9216

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