# How do you simplify sqrt(24x^3yz)?

Sep 23, 2015

$= 2 x \sqrt{6 x y z}$

#### Explanation:

Fully factorising all terms (to assist clarity)

$\sqrt{24 {x}^{3} y z} = \sqrt{2 \cdot 2 \cdot 2 \cdot 3 \cdot x \cdot x \cdot x \cdot y \cdot z}$

Collecting terms that can be expressed as squares

$= \sqrt{{2}^{2} \cdot 2 \cdot 3 \cdot {x}^{2} \cdot x \cdot y \cdot z}$

Taking squared terms outside the square root sign (taking their square roots whilst doing so)

$= 2 x \sqrt{2 \cdot 3 \cdot x \cdot y \cdot z}$

Reforming the compound number from the residua for neatness

$= 2 x \sqrt{6 x y z}$