what is the following quotient?\n$\frac{sqrt3{60}}{sqrt3{20}}$\n$sqrt3{3}$\n$3$\n$2(sqrt3{5})$\n$40$

Explanation:

Step1: Use quotient - rule of radicals

The quotient - rule for radicals states that $\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}$ for $a\geq0$, $b > 0$ and $n\in N,n\geq2$. Here $n = 3$, $a = 60$ and $b = 20$. So, $\frac{\sqrt[3]{60}}{\sqrt[3]{20}}=\sqrt[3]{\frac{60}{20}}$.

Step2: Simplify the fraction inside the radical

Calculate $\frac{60}{20}=3$. Then $\sqrt[3]{\frac{60}{20}}=\sqrt[3]{3}$.

Answer:

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