Question

question 6

simplify: \\(\sqrt3{\frac{64}{343}}\\)

\\(\bigcirc\\ \frac{8}{7}\\)
\\(\bigcirc\\ \frac{4}{49}\\)
\\(\bigcirc\\ \frac{4}{7}\\)
\\(\bigcirc\\ \frac{32}{114}\\)

Explanation:

Apply quotient property of radicals

We rewrite the radical of the fraction as a quotient of two separate radicals.

$$ \sqrt[3]{\frac{64}{343}} = \frac{\sqrt[3]{64}}{\sqrt[3]{343}} $$

Evaluate the numerator

We find the cube root of the numerator.

$$ 64 = 4^3 \implies \sqrt[3]{64} = 4 $$

Evaluate the denominator

We find the cube root of the denominator.

$$ 343 = 7^3 \implies \sqrt[3]{343} = 7 $$

Combine the results

We substitute the simplified values back into the fraction.

$$ \frac{\sqrt[3]{64}}{\sqrt[3]{343}} = \frac{4}{7} $$

Answer:

• (A) \(\frac{8}{7}\)
• (B) \(\frac{4}{49}\)</mcq-correct>
• (C) \(\frac{4}{7}\) (Correct answer)

<mcq-option>(D) \(\frac{32}{114}\)