Trick to find Square root of a number mentally

Today I will be sharing the trick to find the square root of any number (perfect squares only) mentally. But before that just learn this table as you will need it to find the square root.

NUMBER

SQUARE

LAST DIGIT OF SQUARE

0

0

0

1

1

1

2

4

4

3

9

9

4

16

6

5

25

5

6

36

6

7

49

9

8

64

4

9

81

1

Did you notice that last digit for 1 and 9 is same = ’1’. similarly,
For 
2 and 8 it is ’4’.
For 
3 and 7 it is ’9’.
For 
4 and 6 it is ’6’.

 

Trick used

 We will follow these steps to find the Square root of a number:

Example:

Suppose we want to find the square root of 1225.

Step 1:

Ignore last two digits of 1225. Remaining number left is 12.
Step 2:

From the above table square of 3 is less than 12. Therefore left part (L) of our answer will be 3.
Step 3:

Since last digit of  1225 is 5. Therefore right part (R) of our answer will be 5.
Step 4:

Our Answer will be L|R.

Therefore Answer will be 3|5 = 35.

Therefore, 1225 = 35

Example:

Suppose we want to find the square root of 5184.

Step 1:

Ignore last two digits of 5184. Remaining number left is 51.

Step 2:

From the above table square of 7 is less than 51. Therefore left part (L) of our answer will be 7.

Step 3:

Since last digit of  5184 is not equal to 5 or 0. Therefore right part (R) of our answer will not be 5 or 0.

Step 4:

Since last digit of 5184 is 4, Therefore right digit of answer will be either 2 or 8 (see table). Therefore,

[L*(L+1)] = [7*(7+1)] = (7*8) = 56

since 56 is greater than 51, therefore right part of our answer will be 2.

Step 5:

Our Answer will be L|R.

Therefore answer will be 7|2 = 72

Therefore, 5184 = 72