Question

simplify.
remove all perfect squares from inside the square root.
\sqrt{56z^{7}} = \square

Explanation:

Step1: Factor 56 into square factors

$56 = 4 \times 14$, where 4 is a perfect square.

Step2: Rewrite $z^7$ as square factors

$z^7 = z^{6} \times z = (z^3)^2 \times z$, where $(z^3)^2$ is a perfect square.

Step3: Substitute factors into square root

$\sqrt{56z^7} = \sqrt{4 \times 14 \times (z^3)^2 \times z}$

Step4: Separate perfect square terms

$\sqrt{4} \times \sqrt{(z^3)^2} \times \sqrt{14z}$

Step5: Simplify perfect square roots

$\sqrt{4}=2$, $\sqrt{(z^3)^2}=z^3$

Answer:

$2z^3\sqrt{14z}$