# How do you simplify sqrt(512)?

Feb 19, 2016

$= {2}^{\frac{9}{2}}$

#### Explanation:

sqrt(512

We first prime factorise $512$ (ie; express it as a product of its prime factors)

$512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$

$512 = {2}^{9}$

$\sqrt{512} = \sqrt{{2}^{9}}$

$= {2}^{9 \times \frac{1}{2}}$

(note: square root is also called half root)

$= {2}^{\frac{9}{2}}$