Question

write the expression so the radicand has no perfect squares other than 1.
\sqrt{9x^{13}y^{19}}

\sqrt{9x^{13}y^{19}} = \square (type an exact answer, using radicals as needed.)

Explanation:

Step1: Factor into perfect squares

$\sqrt{9x^{12} \cdot x \cdot y^{18} \cdot y}$

Step2: Split radical into products

$\sqrt{9} \cdot \sqrt{x^{12}} \cdot \sqrt{y^{18}} \cdot \sqrt{xy}$

Step3: Simplify perfect square roots

$3 \cdot x^6 \cdot y^9 \cdot \sqrt{xy}$

Step4: Combine terms

$3x^6y^9\sqrt{xy}$

Answer:

$3x^6y^9\sqrt{xy}$