Find the smallest number by which 180 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 180.

To do :

We have to find the smallest number by which 180 should be multiplied so as to get a perfect square.

Solution :

Prime factorisation of 180,

$180=2 \times 2\times 3\times 3\times 5 = 2^2 \times 3^2 \times 5$

To get a perfect square, we have to multiply the factors by 5.

So, $5 \times 2^2 \times 3^2 \times 5$

$ = 2^2 \times 3^2 \times 5^2 = (2 \times 3 \times 5)^2 = (30)^2=900$

$\sqrt{900} = \sqrt{(30)^2} = 30$

Therefore, 180 has to be multiplied by 5 to get a perfect square.

The square root of 900 is 30.