Question

which of the following is equivalent to $60^{\frac{1}{2}}$?\
$\sqrt{60}$\
$\frac{60}{2}$\
$\frac{1}{\sqrt{60}}$\
$\frac{1}{60^2}$

Explanation:

Step1: Recall the exponent rule for fractional exponents

The rule for a fractional exponent \( a^{\frac{m}{n}} \) is \( a^{\frac{m}{n}}=\sqrt[n]{a^m} \). When \( m = 1 \), this simplifies to \( a^{\frac{1}{n}}=\sqrt[n]{a} \).

Step2: Apply the rule to \( 60^{\frac{1}{2}} \)

For \( 60^{\frac{1}{2}} \), we have \( n = 2 \) and \( m = 1 \). Using the rule \( a^{\frac{1}{n}}=\sqrt[n]{a} \), we substitute \( a = 60 \) and \( n = 2 \). So \( 60^{\frac{1}{2}}=\sqrt{60} \).

Answer:

\(\boldsymbol{\sqrt{60}}\) (the first option)