Question

lets practice finding some 5th roots
problem 2.1
$sqrt5{243} = $
check
explain

Explanation:

Step1: Factorize 243

We know that \(243 = 3\times3\times3\times3\times3\), which can be written as \(3^5\) since \(3\times3\times3\times3\times3 = 3^5\).

Step2: Simplify the 5th root

The 5th root of \(3^5\) is given by \(\sqrt[5]{3^5}\). By the property of roots, \(\sqrt[n]{a^n}=a\) when \(n\) is odd (here \(n = 5\) and \(a=3\)). So \(\sqrt[5]{3^5}=3\).

Answer:

\(3\)