Question

assuming ( x ) and ( y ) are both positive, write the following expression in simplest radical form.
( x^{2}sqrt{20x^{7}y^{4}} )

Explanation:

Step1: Factor radicand into perfect squares

$\sqrt{20x^7y^4} = \sqrt{4 \cdot 5 \cdot x^6 \cdot x \cdot y^4}$

Step2: Simplify the radical

$\sqrt{4 \cdot 5 \cdot x^6 \cdot x \cdot y^4} = \sqrt{4} \cdot \sqrt{x^6} \cdot \sqrt{y^4} \cdot \sqrt{5x} = 2x^3y^2\sqrt{5x}$

Step3: Multiply by the external term

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

Step4: Combine like exponents

$2x^{5}y^2\sqrt{5x}$

Answer:

$2x^5y^2\sqrt{5x}$