Square Root of a Perfect Square.

Before describing the method we have to know some basic fundamentals of a perfect square. Watch out this square table from 1-10

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100

 

After watching out we notice that :

(i)            In every perfect square, the unit place will be one number in 1, 4, 5 6, 9 & 0  

(Note it doesn’t mean that every number which ends with these number will always be a perfect Square).

(ii)          It is definite that in any number, if unit place is 2, 3, 7 & 8 that number is not a perfect square.

(iii)         With respect to unit place value there may be chance that the unit place value of the square root of that number will be like that :

Unit Place number of square	Unit place number of square root
1	1 or 9
4	2 or 8
5	5
6	4 or 6
9	3 or 7
10	0

Now method to find out square root of a perfect square .

Example 1: Square root of 5776= ?

Step 1. First make two pairs of numbers in 5776. First will be a pair of 2 digits from right side, and second will be remaining digits. So pair will be 57 76.

Step 2. Now take a number which is a square root of a perfect square just less than 57. Here we take 7. Because 7²=49 and 49 is less than 57

Step 3. Because unit place of 5776 is 6 that is why the square root will be either 74 or 76. So which is the correct option for that there are also two methods :

(i)            57-49=8 and 8 is greater than 7. That is why square root will be of greater value, means 76 is the correct option. If we get less than value than option will also be of lesser value.

(ii)          75 comes between 74 and 76. And square of 75 is 5625 which is less than 5776, that is why the square root will be of greater value.   
                     

(Finding out square of a number like 75 which ends with 5 is only 2 seconds job.Trick for that I’ll describe in another post.)

Let us take another Example :

Example 2: Find out Square root of 8464.

Step 1 : 84 64

Step 2: 9²=81 and 81 is less than 84.

Step 3: Options are 92 or 98 (But 84-81=3 and 3 is less than 9. So our option will be of lesser value)

Step 4: Answer 92