Question

lets practice finding some 5th roots
problem 2.3
\sqrt5{\frac{1}{32}} =
check
explain

Explanation:

Step1: Recall the 5th root property

The 5th root of a fraction \(\sqrt[5]{\frac{a}{b}}\) can be written as \(\frac{\sqrt[5]{a}}{\sqrt[5]{b}}\) (where \(b
eq0\)). So, \(\sqrt[5]{\frac{1}{32}}=\frac{\sqrt[5]{1}}{\sqrt[5]{32}}\).

Step2: Calculate the 5th roots

We know that \(\sqrt[5]{1} = 1\) (since \(1^5=1\)) and \(\sqrt[5]{32}\): we need to find a number \(x\) such that \(x^5 = 32\). We know that \(2^5=32\) (because \(2\times2\times2\times2\times2 = 32\)), so \(\sqrt[5]{32}=2\).

Step3: Simplify the fraction

Substituting the values of the 5th roots into the fraction \(\frac{\sqrt[5]{1}}{\sqrt[5]{32}}\), we get \(\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)