Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $sqrt{4x^{7}y^{7}}$

Explanation:

Step1: Split radical into factors

$\sqrt{4x^7y^7} = \sqrt{4} \cdot \sqrt{x^7} \cdot \sqrt{y^7}$

Step2: Simplify perfect square factors

$\sqrt{4}=2$, $\sqrt{x^7}=\sqrt{x^6 \cdot x}=x^3\sqrt{x}$, $\sqrt{y^7}=\sqrt{y^6 \cdot y}=y^3\sqrt{y}$

Step3: Combine simplified terms

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

Answer:

$2x^3y^3\sqrt{xy}$