Question

simplify.
\sqrt4{\frac{16}{625}}
be sure to write your answer in lowest terms.

Explanation:

Step1: Recall nth root property

For a fourth root, \(\sqrt[4]{\frac{a}{b}}=\frac{\sqrt[4]{a}}{\sqrt[4]{b}}\) (where \(a\geq0,b > 0\)). So \(\sqrt[4]{\frac{16}{625}}=\frac{\sqrt[4]{16}}{\sqrt[4]{625}}\).

Step2: Simplify fourth roots

We know that \(2^4 = 16\), so \(\sqrt[4]{16}=2\). Also, \(5^4=625\), so \(\sqrt[4]{625} = 5\).

Step3: Form the fraction

Substituting the values, we get \(\frac{2}{5}\).

Answer:

\(\frac{2}{5}\)