Question

question
assuming x and y are both positive, write the following expression in simplest radical form.
y^{2}\sqrt{175x^{7}y^{2}}
answer attempt 1 out of 2

Explanation:

Step1: Factor radicand into perfect squares

$\sqrt{175x^7y^2} = \sqrt{25 \cdot 7 \cdot x^6 \cdot x \cdot y^2}$

Step2: Simplify the square root

$\sqrt{25 \cdot 7 \cdot x^6 \cdot x \cdot y^2} = 5x^3y\sqrt{7x}$

Step3: Multiply by outer term $y^2$

$y^2 \cdot 5x^3y\sqrt{7x} = 5x^3y^{2+1}\sqrt{7x}$

Step4: Combine like terms for $y$

$5x^3y^{3}\sqrt{7x}$

Answer:

$5x^3y^3\sqrt{7x}$