Question

1. what is the radical equivalent to \\(s^{\frac{3}{2}}\\)?

\\(\sqrt3{s^2}\\)

\\(\sqrt{s^3}\\)

\\(\sqrts{2^3}\\)

\\(\sqrts{3^2}\\)

Explanation:

Identify the given expression

We are given the exponential expression \(s^{\frac{3}{2}}\) and need to find its equivalent radical form.

Apply the conversion rule

Using the Radical to Rational Exponent Conversion knowledge point

$$ x^{\frac{m}{n}} = \sqrt[n]{x^m} $$

Convert the expression

Using the Radical to Rational Exponent Conversion knowledge point

$$ s^{\frac{3}{2}} = \sqrt[2]{s^3} = \sqrt{s^3} $$

Match with the options

The equivalent radical expression is \(\sqrt{s^3}\), which corresponds to the second option.

Answer:

• (A) \(\sqrt[3]{s^2}\)
• (B) \(\sqrt{s^3}\) (Correct answer)
• (C) \(\sqrt{2^3}\)
• (D) \(\sqrt[s]{3^2}\)