Question

which expression is equivalent to \\(\frac{\sqrt{2}}{\sqrt3{2}}\\)?

• \\(\frac{1}{4}\\)
• \\(\sqrt6{2}\\)
• \\(\sqrt{2}\\)
• \\(\frac{\sqrt{2}}{2}\\)

Explanation:

Convert radicals to exponential form

Using the Radical to Exponential Form and Rational Exponents knowledge points

$$
LATEXBLOCK0
$$

Apply exponent division rule

Using the Exponent Rules knowledge point

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

Simplify the exponent fraction

Using the Algebraic Simplification knowledge point

$$ \frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6} $$

Convert back to radical form

Using the Radical to Exponential Form knowledge point

$$ 2^{\frac{1}{6}} = \sqrt[6]{2} $$

Answer:

• (A) \(\frac{1}{4}\)
• (B) \(\sqrt[6]{2}\) (Correct answer)
• (C) \(\sqrt{2}\)
• (D) \(\frac{\sqrt{2}}{2}\)