Question

which expression is equivalent to \frac{\sqrt4{6}}{\sqrt3{2}}?

\circ \frac{\sqrt12{27}}{2}
\circ \frac{\sqrt4{24}}{2}
\circ \frac{\sqrt12{55296}}{2}
\circ \frac{\sqrt12{177147}}{3}

Explanation:

Convert radicals to rational exponents

Using the Radical to Exponential Form and Rational Exponents knowledge points

$$ \frac{\sqrt[4]{6}}{\sqrt[3]{2}} = \frac{6^{1/4}}{2^{1/3}} $$

Find a common denominator for the exponents

Using the Rational Exponents knowledge point

$$
LATEXBLOCK0
$$

Rationalize the denominator

Using the Rationalizing the Denominator knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) \(\frac{\sqrt[12]{27}}{2}\)
• (B) \(\frac{\sqrt[4]{24}}{2}\)
• (C) \(\frac{\sqrt[12]{55296}}{2}\) (Correct answer)
• (D) \(\frac{\sqrt[12]{177147}}{3}\)