Question

simplify. remove all perfect squares from inside the square root. assume ( z ) is positive. (sqrt{72z^{5}}=)

Explanation:

Step1: Factor into perfect squares

$\sqrt{72z^5} = \sqrt{36 \times 2 \times z^4 \times z}$

Step2: Split the square root

$\sqrt{36} \times \sqrt{z^4} \times \sqrt{2z}$

Step3: Simplify perfect square roots

$6 \times z^2 \times \sqrt{2z}$

Step4: Combine terms

$6z^2\sqrt{2z}$

Answer:

$6z^2\sqrt{2z}$