Question

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
​

Answer 1

$\sf{\underline{To\:find:}}$

The smallest number by which 3645 must be divided so that it becomes a perfect square.

$\sf{\underline{First\:of\:all:}}$

Find the prime factors of: $\boxed{\sf{3645}}$

$\sf{\underline{So,\:here\:we\:go:}}$

$\boxed{\sf{3645 = 5 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3}}$

Organising the prime factors into pairs,

$\sf{\underline{We\:get:}}$

$\boxed{\sf{3645 = (3 \times 3)(3 \times 3)(3 \times 3) \times 5}}$

$\sf{\underline{Note:}}$ 5 doesn't exist in pair.

$\sf{\underline{So:}}$

The smallest number that should be divided from 3645 to make it a perfect square is 5.

$\sf{\underline{Therefore:}}$

$\boxed{\sf{\frac{3645}{5} = 729}}$

$\sf{\underline{Hence:}}$

The resulting number is 729.

$\boxed{\sf{ \sqrt{729} = 27}}$

$\sf{\underline{Therefore:}}$

27 is the square root of resulting number 729.