Question

write the expression so the radicand has no perfect squares other than 1.
\sqrt{63x^{9}}

\sqrt{63x^{9}} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Factor radicand into squares

$\sqrt{63x^9} = \sqrt{9 \cdot 7 \cdot x^8 \cdot x}$

Step2: Separate perfect square factors

$\sqrt{9} \cdot \sqrt{x^8} \cdot \sqrt{7x}$

Step3: Simplify perfect square roots

$3 \cdot x^4 \cdot \sqrt{7x}$

Answer:

$3x^4\sqrt{7x}$