Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form.
$2x^{2}\sqrt{175x^{5}y^{3}}$

Explanation:

Step1: Factor radicand into perfect squares

$\sqrt{175x^6y^3} = \sqrt{25 \times 7 \times (x^3)^2 \times y^2 \times y}$

Step2: Simplify the square root

$\sqrt{25 \times 7 \times (x^3)^2 \times y^2 \times y} = 5x^3y\sqrt{7y}$

Step3: Multiply with the outside term

$2x^2 \times 5x^3y\sqrt{7y} = (2 \times 5)x^{2+3}y\sqrt{7y}$

Step4: Compute coefficients and exponents

$10x^5y\sqrt{7y}$

Answer:

$10x^5y\sqrt{7y}$