How to find Square Root of Perfect Squares Quickly: Today we will discuss a vedic maths trick to find out square root of perfect
squares quickly. This method uses the same approach which we have seen in the
cube root method.
To proceed its very necessary for us to memorize the
square of first ten natural numbers.
Number

Square

1

1

2

4

3

9

4

16

5

25

6

36

7

49

8

64

9

81

10

100

From the above table you can observe that we have 1 in the number column and
1 in the square column. In the same way, in the 9th row we have 9 in the number
column and 1 in the square column. From this we can conclude that if the number
ends in 1, the square root ends in 1 or 9 . Similarly if the number ends in 4
the square root ends in 2 or 8. If the number ends in 9, the square root ends
in 3 or 7. If the number ends in 6, the square root ends in 4 or 6. If the
number ends in 5, the square root ends in 5. If the number ends in 0, the
square root also ends in 0. The below table summarize this thing. You
should memorize this table.
Last digit of square

Last digit of square root

1

1 or 9

4

2 or 8

9

3 or 7

6

4 or 6

5

5

0

0

From the above tables you can find that a perfect square never ends
with 2,3,7, or 8
Below is the another table of square of numbers from 10 to 100. This
table will help us to find the square roots quickly.
Number

Square

10

100

20

400

30

900

40

1600

50

2500

60

3600

70

4900

80

6400

90

8100

100

10000

Lets now try to find the square root of 9801
Step 1: The last digit of the number 9801 is 1 therefore
the last digit of the square root will be either 1 0r 9. The answer for now
will be _1 or _9
Step: 2 The number 9801 lies between 8100 (square of 90)
and 10000 ( square of 100). Therefore the answer lies between 90 and 100.
From the first step we know that the square ends in either 1
or 9. So the answer can be 91 or 99
Step 3: Now we pick the number which is closer to the
square. Since 9801 is closer to the bigger number 10,000 we will take the
number number 99 as the answer. So our answer becomes 99
Lets find the square root of 5184 through the same shortcut method
Step 1: Number ends in 4. So square root ends in either 2
or 8. Answer at this stage can be _2 or _8
Step 2: 5184 lies between 4900 and 6400, the square of 70
and 80. From the first step the answer at this stage becomes 72 or 78
Step 3: 5184 is closer to the smaller number 4900. Thus we
take smaller number 72 as our correct answer.
I hope you have understood the method, if you have any problem let us know
in comments and we will do our best to help you.