Find the cube root of frac{512}{3375}. | vedclass

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Question

(C) To find the cube root of $\frac{512}{3375}$,we calculate the cube roots of the numerator and the denominator separately.First,find the prime facto

Vedclass · Accepted Answer

$\frac{8}{15}$

Vedclass · Answer

(C) To find the cube root of $\frac{512}{3375}$,we calculate the cube roots of the numerator and the denominator separately.First,find the prime factorization of $512$:$512 = 2^9 = (2^3)^3 = 8^3$.So,$\sqrt[3]{512} = 8$.Next,find the prime factorization of $3375$:$3375 = 3^3 	imes 5^3 = (3 	imes 5)^3 = 15^3$.So,$\sqrt[3]{3375} = 15$.Therefore,$\sqrt[3]{\frac{512}{3375}} = \frac{\sqrt[3]{512}}{\sqrt[3]{3375}} = \frac{8}{15}$.

Find the cube root of $\frac{512}{3375}$.

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