Question

what is the following quotient?
\\(\frac{\sqrt{120}}{\sqrt{30}}\\)
\\(\bigcirc\\) 2
\\(\bigcirc\\) 4
\\(\bigcirc\\) \\(2\sqrt{10}\\)
\\(\bigcirc\\) \\(3\sqrt{10}\\)

Explanation:

Step1: Use the quotient rule for square roots

The quotient rule for square roots states that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ (where $a\geq0$ and $b>0$). So we can rewrite $\frac{\sqrt{120}}{\sqrt{30}}$ as $\sqrt{\frac{120}{30}}$.

Step2: Simplify the fraction inside the square root

Calculate $\frac{120}{30}$, which equals $4$. So now we have $\sqrt{4}$.

Step3: Evaluate the square root

The square root of $4$ is $2$, since $2\times2 = 4$.

Answer:

A. 2