Find the smallest number by which 1458 should be multiplied so as to get a perfect square. Also, find the square root of the square number obtained.

Given :

The given number is 1458.

To do :

We have to find the smallest number by which 1458 should be multiplied so as to get a perfect square.

Solution :

Prime factorisation of 1458,

$1458=2 \times 3\times 3\times 3\times 3\times 3\times 3 = 2 \times 3^2 \times 3^2 \times 3^2$

To get a perfect square, we have to multiply the factors by 2.

So, $2 \times 2 \times 3^2 \times 3^2 \times 3^2$

$ = 2^2 \times 3^2 \times 3^2 \times 3^2 = 4 \times 729 = 2916$

$\sqrt{2916} = \sqrt{2^2 \times 27^2} = 2 \times 27 = 54$

Therefore, 1458 has to be multiplied by 2 to get a perfect square.

The square root of 2916 is 54.