If $\sqrt{y} = 64 x^{3}$ $sqrty=64x^3$ , then what is $\sqrt[3]{y}$ $root(3)y$ ?

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If $\sqrt{y} = 64 x^{3}$ $sqrty=64x^3$ , then what is $\sqrt[3]{y}$ $root(3)y$ ?

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Answer 1 · 2017-02-09T10:22:45

$16 x^{2}$ $16x^2$

Explanation:

If we have

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

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

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

${(\sqrt{y})}^{\frac{2}{3}} = {(64 x^{3})}^{\frac{2}{3}}$ $(sqrty)^(2/3)=(64x^3)^(2/3)$

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

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

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If $\sqrt{y} = 64 x^{3}$ $sqrty=64x^3$ , then what is $\sqrt[3]{y}$ $root(3)y$ ?

1 Answer

Explanation:

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