Question

which expression is equivalent to \\(\sqrt{5}\\)? \\(2^{\frac{1}{5}}\\) \\(5^2\\) \\(5^{\frac{1}{2}}\\) \\(2^5\\)

Explanation:

Step1: Recall radical-exponent rule

The rule for converting a square root (radical) to a rational exponent is $\sqrt[n]{a}=a^{\frac{1}{n}}$. For a square root, $n = 2$, so $\sqrt{a}=a^{\frac{1}{2}}$.

Step2: Apply rule to $\sqrt{5}$

Using the rule, $\sqrt{5}=5^{\frac{1}{2}}$.

Answer:

$5^{\frac{1}{2}}$ (corresponding to the option "5^(1/2)")