Question

simplify.
\sqrt3{\frac{343}{64}}
be sure to write your answer in lowest terms.

Explanation:

Step1: Recall cube root property

The cube root of a fraction $\sqrt[3]{\frac{a}{b}}$ can be written as $\frac{\sqrt[3]{a}}{\sqrt[3]{b}}$, where $a = 343$ and $b = 64$.

Step2: Find cube roots of numerator and denominator

We know that $7^3 = 343$, so $\sqrt[3]{343}=7$. Also, $4^3 = 64$, so $\sqrt[3]{64}=4$.

Step3: Form the fraction

Using the property from Step 1, $\sqrt[3]{\frac{343}{64}}=\frac{\sqrt[3]{343}}{\sqrt[3]{64}}=\frac{7}{4}$.

Answer:

$\frac{7}{4}$