Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $y^{2}\sqrt{25x^{7}y^{7}}$

Explanation:

Step1: Simplify the radical's constant factor

$\sqrt{25x^7y^7} = \sqrt{25} \cdot \sqrt{x^7} \cdot \sqrt{y^7} = 5 \cdot \sqrt{x^7} \cdot \sqrt{y^7}$

Step2: Simplify variable radicals

$\sqrt{x^7} = x^{\frac{7}{2}} = x^3\sqrt{x}$, $\sqrt{y^7} = y^{\frac{7}{2}} = y^3\sqrt{y}$

Step3: Combine with external term

$y^2 \cdot 5x^3y^3\sqrt{xy} = 5x^3y^{2+3}\sqrt{xy}$

Step4: Simplify exponent of $y$

$5x^3y^5\sqrt{xy}$

Answer:

$5x^3y^5\sqrt{xy}$