Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.

Given :

The given number is 3645.

To do :

We have to find the smallest number by which 3645 must be divided so that it becomes a perfect square and also the square root of the number so obtained.

Solution :

Prime factorisation of 3645,

$3645=3\times3\times3\times3\times3\times3\times5$

$= 3^2 \times3^2\times3^2\times5$

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

So, $3^2 \times 3^2 \times 3^2\times5\div5= 3^2 \times 3^2\times3^2\times1 $

$= (3 \times3\times3)^2 $

$= (27)^2$

$=729$

$\sqrt{729} = \sqrt{(27)^2}$

$= 27$

Therefore, 729 has to be divided by 5 to get a perfect square.

The square root of 729 is 27.