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

Sep 23, 2017

$\sqrt{576} = 24$

#### Explanation:

Given:

$16 \times 36 = 576$

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

$16 \times 36 = 576$

$\therefore 4 \times 4 \times 6 \times 6 = 576$

$\therefore \left(4 \times 6\right) \times \left(4 \times 6\right) = 576$

$\therefore {\left(4 \times 6\right)}^{2} = 576$

$\therefore {\left(24\right)}^{2} = 576$

Hence:

$\sqrt{576} = 24$