To determine the equivalent expression to [tex]\( 60^{\frac{1}{2}} \)[/tex], let's consider what this notation represents.
The notation [tex]\( a^{b} \)[/tex] refers to [tex]\( a \)[/tex] raised to the power of [tex]\( b \)[/tex]. When the exponent [tex]\( b \)[/tex] is written as a fraction [tex]\( \frac{m}{n} \)[/tex], it can be interpreted as the [tex]\( n \)[/tex]-th root of [tex]\( a \)[/tex] raised to the power of [tex]\( m \)[/tex]. Specifically, [tex]\( a^{\frac{1}{2}} \)[/tex] means the square root of [tex]\( a \)[/tex].
So, [tex]\( 60^{\frac{1}{2}} \)[/tex] is the same as the square root of 60, which is written as [tex]\( \sqrt{60} \)[/tex].
Let's analyze the options provided:
1. [tex]\(\frac{60}{2}\)[/tex]: This evaluates to 30, which is clearly not the same as the square root of 60.
2. [tex]\(\sqrt{60}\)[/tex]: This is the notation for the square root of 60, which is what we are looking for.
3. [tex]\(\frac{1}{60^2}\)[/tex]: This is the reciprocal of 3600, which is not related to the square root of 60.
4. [tex]\(\frac{1}{\sqrt{60}}\)[/tex]: This is the reciprocal of the square root of 60, which is not the same as the square root of 60 itself.
Therefore, the expression that is equivalent to [tex]\( 60^{\frac{1}{2}} \)[/tex] is [tex]\(\sqrt{60}\)[/tex].
