Question

simplify.
remove all perfect squares from inside the square roots. assume ( x ) and ( z ) are positive.
( sqrt{72x^3z^3} = )

Explanation:

Step1: Factor into perfect squares

$\sqrt{36 \cdot 2 \cdot x^2 \cdot x \cdot z^2 \cdot z}$

Step2: Separate square root terms

$\sqrt{36} \cdot \sqrt{x^2} \cdot \sqrt{z^2} \cdot \sqrt{2xz}$

Step3: Simplify perfect square roots

$6 \cdot x \cdot z \cdot \sqrt{2xz}$

Answer:

$6xz\sqrt{2xz}$