Question

Simplify.

Answer 1

Answer:

$\huge\boxed{\sqrt{72z^5}=6z^2\sqrt{2z}}$

Step-by-step explanation:

$72=(36)(2)=(6^2)(2)\\\\z^5=z^{2+2+1}=(z^2)(z^2)(z^1)\qquad\text{used}\ (a^n)(a^m)=a^{n+m}\\\\\sqrt{72z^5}=\sqrt{(6^2)(2)(z^2)(z^2)(z)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{72z^5}=\sqrt{6^2}\cdot\sqrt{z^2}\cdot\sqrt{z^2}\cdot\sqrt{2z}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\\sqrt{72z^5}=(6)(z)(z)\sqrt{2z}\\\\\sqrt{72z^5}=6z^2\sqrt{2z}$