Quants: Square and square roots

Here are some tips on square and square roots that will help you in solving the quants section in GRE.

• The numbers ending with 2, 3, 7, 8 can never be perfect squares.

• The no. of zeroes in the end of a perfect square cannot be odd.

e.g.
400, 120000 are perfect squares.
But, 6000, 800000 can never be perfect squares.

• If we take a two digit no. ending with '5', their squares can be found out in the following ways:

15^2 = 1 * 2(100) + (5^2) = 225
25^2 = 2 * 3(100) + (5^2) = 625
85^2 = 8 * 9(100) + (5^2) = 7225

• For the nos. containing '1', their squares can be found out by:

1^2 = 1
11^2 = 121
1111^2 = 1234321

(Just count the no. of 1s. If there are three 1s, just go on from 1 to 3 as in '123' and then return back to 1. So, the square of 111 is 12321.)

You can share your tips on/about the squares and square roots in this thread. 😀