Question

Write the given surd $\sqrt[4]{4\frac{400}{49}}$ in its simplest form.

Answer 1

Resolving $\sqrt[4]{4\frac{400}{49}}$ into the prime factors, we get,

$\Rightarrow \sqrt[4]{4\frac{400}{49}}=\sqrt[4]{4\frac{2^4\times 5^2}{7^2}}$

Simplifying the powers, we get,

$2\sqrt[4]{4\frac{5^2}{7^2}}=2\sqrt{\frac{5}{7}}$, which is the simplest form.