Question

Given that `16 xx 36=576`, then find `sqrt(576)` without a calculator using properties of perfect squares?

Answer 1

`sqrt(576) = 24`

Explanation:

Given:

`16 xx 36 = 576`

Then we can manipulate the LHS, noting that both `16` and `36` are perfect squares to get:

`16 xx 36 = 576`

`:. 4 xx 4 xx 6 xx 6 = 576`

`:. (4 xx 6) xx (4 xx 6) = 576`

`:. (4 xx 6)^2 = 576`

`:. (24)^2 = 576`

Hence:

`sqrt(576) = 24`