Question

match each radical expression with the equivalent exponential expression.

\\(\sqrt5{2}\\)
\\(\sqrt{3}\\)
\\(\sqrt3{3}\\)
\\(\sqrt{2}\\)

options to match:
\\(2^{\frac{1}{5}}\\), \\(2^{\frac{1}{2}}\\), \\(3^{\frac{1}{4}}\\), \\(5^{\frac{1}{2}}\\), \\(3^{\frac{1}{3}}\\), \\(4^{\frac{1}{3}}\\)

Explanation:

Step1: Convert the first radical expression

$$\sqrt[5]{2} = 2^{\frac{1}{5}}$$

Step2: Convert the second radical expression

$$\sqrt{3} = 3^{\frac{1}{2}}$$

Step3: Convert the third radical expression

$$\sqrt[3]{3} = 3^{\frac{1}{3}}$$

Step4: Convert the fourth radical expression

$$\sqrt[2]{2} = 2^{\frac{1}{2}}$$

Answer:

\(\sqrt[5]{2}\) matches with \(2^{\frac{1}{5}}\)
\(\sqrt{3}\) matches with \(3^{\frac{1}{2}}\)
\(\sqrt[3]{3}\) matches with \(3^{\frac{1}{3}}\)
\(\sqrt[2]{2}\) matches with \(2^{\frac{1}{2}}\)