Question

select the correct answer.
which expression is equivalent to $sqrt3{56x^{7}y^{5}}$, if $x \
eq 0$ and $y \
eq 0$
a. $2x^{2}y\sqrt3{7xy^{2}}$
b. $8xy\sqrt3{7x^{4}y^{2}}$
c. $8x^{2}y\sqrt3{7xy^{2}}$
d. $2x^{4}y^{2}\sqrt3{7}$

Explanation:

Step1: Factor the radicand

$\sqrt[3]{56x^7y^5} = \sqrt[3]{8 \times 7 \times x^6 \times x \times y^3 \times y^2}$

Step2: Extract perfect cubes

$\sqrt[3]{8x^6y^3} \times \sqrt[3]{7xy^2} = 2x^2y\sqrt[3]{7xy^2}$

Answer:

A. $2x^2y\sqrt[3]{7xy^2}$