Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $4xy^{2}\sqrt{252x^{6}y^{4}}$

Explanation:

Step1: Factor radicand into squares

$\sqrt{252x^6y^4} = \sqrt{36 \times 7 \times (x^3)^2 \times (y^2)^2}$

Step2: Simplify the radical

$\sqrt{36} \times \sqrt{7} \times \sqrt{(x^3)^2} \times \sqrt{(y^2)^2} = 6x^3y^2\sqrt{7}$

Step3: Multiply with outer terms

$4xy^2 \times 6x^3y^2\sqrt{7} = (4 \times 6) \times (x \times x^3) \times (y^2 \times y^2) \times \sqrt{7}$

Step4: Compute coefficients and exponents

$24x^{1+3}y^{2+2}\sqrt{7} = 24x^4y^4\sqrt{7}$

Answer:

$24x^4y^4\sqrt{7}$