Question

Which one of the following perfect square numbers, is the square of an even number? 121, 625, 169, 1296.
$
  (a){\text{ 625}} \\
  (b){\text{ 169}} \\
  (c){\text{ 1296}} \\
  (d){\text{ 121}} \\
 $

Answer 1

Hint – In this problem use the approach that since the square of an even number is also even thus the square root of an even number will be even only. Hence check for the even number amongst the given numbers and that will simply be the answer.

Complete step-by-step solution -
Given perfect squares are
121, 625, 169, 1296.
As we know, an even number is always divisible by 2 but an odd number is not divisible by 2.
So the square of the even number is also even and it is also divisible by 2.
For example 6 is an even number, the square of 6 is 36 which is again an even number and 36 is divisible by 2.
So from the given perfect squares only 1296 is even.
So find out its square root of 1296.
$\sqrt {1296} = \sqrt {{{\left( {36} \right)}^2}} = 36$
So as we see 36 is an even number and divisible by 2.
So from among perfect squares only 1296 is the square of an even number.
So this is the required answer.
Hence option (C) is correct.

Note – This problem could have been solved using another method, if we find the square root of each given number then check for their square root to be even or odd keeping one thing in mind that it would be even if and only it is completely divisible by 2, then we could have reached the right answer too, but it’s a length method hence not preferred.