FIND SQUARE ROOT OF A NUMBER
Important observations

Perfect square of a number never ends in 2,3,7,8.

Perfect square ends in 1,4,5,6,9,0.
Perfect Square Ends in
1
4
5
6
9
0
Square Root Ends in
1 or 9
2 or 8
5
4 or 6
3 or 7
0
EXAMPLE1:
Find The Square Root of 6889
Step1: X=6889
Step2: √6889
Step3: Split the number in to two groups from left as below
68/89
Step4: Number of digits in square root is =number of groups in that number
The above number has 2 digits in the square root
Step5: Now consider the group from the right i.e 68
68 lies between 8² and 9² and the last digit of 6889 ends in 9 so root ends in 3 or 7
Step6: Take 8 has first digit of square toot since it lies between 8² and 9² now the question is whether 3 or 7 in last digit i.e 83 or 87
Step7: In vedic math tricks1 we had discussed how to find square of a number ends in 5
Step8: Consider 85 square of 85 is 7225 which is bigger than 6889 so 87 is even bigger
Step9: Now we got the answer i.e 83
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