Which of the following perfect squares are squares of even numbers?
25, 64, 100, 169, 256, 289, 961, 1296, 6561, 8100.
Which of the following perfect squares are squares of odd numbers?
36, 49, 64, 81, 100, 121, 169, 484, 625, 900, 1296, 1681.

$2^2=4, 4^2=16, 6^2=36, 8^2 =64, 10^2=100.$

Given :

Two sets of squares are given.

To do:

We have to find which of the given numbers are squares of even numbers and odd numbers.

Solution :

Square of even number always ends with 2, 6, and 4.

$2^2 = 4, 4^2 = 16, 6^2 =36, 8^2 = 64, 12^2 = 144 $

Square of even number always ends with 1, 9, and 5.

$1^2 = 1, 3^2 = 9, 5^2 = 25, 7^2=49, 9^2=81, 11^2=121$

Therefore,

In the first set 64,100,256,1296 and 8100 are squares of even numbers.

In the second set 49,81,121,169,625 and 1681 are squares of odd numbers.

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Updated on: 10-Oct-2022

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