Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $sqrt{36x^3y^7}$

Explanation:

Step1: Split the radical into factors

$\sqrt{36x^3y^7} = \sqrt{36} \cdot \sqrt{x^3} \cdot \sqrt{y^7}$

Step2: Simplify each radical factor

$\sqrt{36}=6$, $\sqrt{x^3}=\sqrt{x^2 \cdot x}=x\sqrt{x}$, $\sqrt{y^7}=\sqrt{y^6 \cdot y}=y^3\sqrt{y}$

Step3: Multiply the simplified terms

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

Answer:

$6xy^3\sqrt{xy}$