Answer
$3x^6y^5\sqrt{2y}$
Work Step by Step
We are asked to simplify:
$\sqrt{x^5y^5}3\sqrt{2x^7y^6}$
Recall the property (pg. 367):
$\sqrt[n]{a}*\sqrt[n]{b}=\sqrt[n]{ab}$ (if $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers)
Applying this property, we get:
$=3\sqrt{2x^5x^7y^5y^6}$
Using the property that $x^ax^b=x^{a+b}$, we get:
$=3\sqrt{2x^{12}y^{11}}$
$=3\sqrt{2x^{12}y^{10}y^1}$
Splitting up the square root, we get:
$=3\sqrt{x^{12}}\sqrt{y^{10}}\sqrt{2y}$
$=3\sqrt{(x^6)^2} \cdot \sqrt{(y^5)^2}\cdot \sqrt{2y}$
$=3x^6y^5\sqrt{2y}$
