Question

question
express $6^{\frac{1}{2}}$ in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Recall the exponent - radical rule

The rule for converting a fractional exponent to a radical is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\). When \(m = 1\), the formula simplifies to \(a^{\frac{1}{n}}=\sqrt[n]{a}\).
For the expression \(6^{\frac{1}{2}}\), we have \(a = 6\), \(n=2\) and \(m = 1\).

Step2: Apply the rule

Using the rule \(a^{\frac{1}{n}}=\sqrt[n]{a}\) with \(a = 6\) and \(n = 2\), we get \(6^{\frac{1}{2}}=\sqrt{6}\). Since 6 does not have any perfect - square factors other than 1, \(\sqrt{6}\) is in the simplest radical form.

Answer:

\(\sqrt{6}\)