Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.

Given :

The given number is 147.

To do :

We have to find the smallest number by which 147 should be multiplied so as to get a perfect square and also the square root of the number so obtained.

Solution :

Prime factorisation of 147,

$147=3\times7\times7$

$= 3 \times 7^2$

To get a perfect square, we have to multiply the factors by 3.

So, $3 \times 7^2 \times 3= 3^2 \times 7^2 $

$= (3 \times 7)^2 $

$= (21)^2$

$=441$

$\sqrt{441} = \sqrt{(21)^2}$

$= 21$

Therefore, 147 has to be multiplied by 3 to get a perfect square.

The square root of 441 is 21.