select the correct answer. which expression is equivalent to $sqrt3{56x^{7}y^{5}}$, if $x\neq0$ and…

select the correct answer. which expression is equivalent to $sqrt3{56x^{7}y^{5}}$, if $x\neq0$ and $y\neq0$?\na. $2x^{2}ysqrt3{7xy^{2}}$\nb. $8xysqrt3{7x^{4}y^{2}}$\nc. $8x^{2}ysqrt3{7xy^{2}}$\nd. $2x^{4}y^{2}sqrt3{7}$

select the correct answer. which expression is equivalent to $sqrt3{56x^{7}y^{5}}$, if $x\neq0$ and $y\neq0$?\na. $2x^{2}ysqrt3{7xy^{2}}$\nb. $8xysqrt3{7x^{4}y^{2}}$\nc. $8x^{2}ysqrt3{7xy^{2}}$\nd. $2x^{4}y^{2}sqrt3{7}$

Answer

Answer:

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

Explanation:

Step1: Prime - factorize the coefficient

We have $\sqrt[3]{56x^{7}y^{5}}=\sqrt[3]{2^{3}\times7\times x^{6}\times x\times y^{3}\times y^{2}}$.

Step2: Use the property $\sqrt[3]{abc}=\sqrt[3]{a}\cdot\sqrt[3]{b}\cdot\sqrt[3]{c}$

$\sqrt[3]{2^{3}\times7\times x^{6}\times x\times y^{3}\times y^{2}}=\sqrt[3]{2^{3}}\cdot\sqrt[3]{7}\cdot\sqrt[3]{x^{6}}\cdot\sqrt[3]{x}\cdot\sqrt[3]{y^{3}}\cdot\sqrt[3]{y^{2}}$.

Step3: Simplify each cube - root

$\sqrt[3]{2^{3}} = 2$, $\sqrt[3]{x^{6}}=x^{2}$, $\sqrt[3]{y^{3}} = y$. So, $\sqrt[3]{2^{3}}\cdot\sqrt[3]{7}\cdot\sqrt[3]{x^{6}}\cdot\sqrt[3]{x}\cdot\sqrt[3]{y^{3}}\cdot\sqrt[3]{y^{2}}=2x^{2}y\sqrt[3]{7xy^{2}}$.