# If sqrty=64x^3, then what is root(3)y?

$16 {x}^{2}$

#### Explanation:

If we have

$\sqrt{y} = 64 {x}^{3}$

then what is the value of $\sqrt[3]{y}$?

We can do this by squaring then taking the cube root of y, in effect taking both sides to the power of $\frac{2}{3}$:

${\left(\sqrt{y}\right)}^{\frac{2}{3}} = {\left(64 {x}^{3}\right)}^{\frac{2}{3}}$

We can use the rule that ${\left({x}^{a}\right)}^{b} = {x}^{a b}$

$\sqrt[3]{y} = {\left({2}^{6} {x}^{3}\right)}^{\frac{2}{3}} = {2}^{6 \times \left(\frac{2}{3}\right)} {x}^{3 \times \left(\frac{2}{3}\right)} = {2}^{4} {x}^{2} = 16 {x}^{2}$