Question

what is the following quotient?
\\(\frac{sqrt3{60}}{sqrt3{20}}\\)
\\(\circ\\) \\(sqrt3{3}\\)
\\(\circ\\) 3
\\(\circ\\) \\(2\left(\sqrt3{5}\
ight)\\)
\\(\circ\\) 40

Explanation:

Step1: Recall the property of cube roots

The property of cube roots states that $\frac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\frac{a}{b}}$ for any real numbers $a$ and $b$ (where $b
eq0$). So we can apply this property to the given expression $\frac{\sqrt[3]{60}}{\sqrt[3]{20}}$.

Step2: Simplify the fraction inside the cube root

We have $\frac{\sqrt[3]{60}}{\sqrt[3]{20}}=\sqrt[3]{\frac{60}{20}}$. Now, simplify the fraction $\frac{60}{20}$. Since $60\div20 = 3$, the expression becomes $\sqrt[3]{3}$.

Answer:

$\sqrt[3]{3}$ (corresponding to the option $\boldsymbol{\sqrt[3]{3}}$)