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 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 $\frac{120}{30}=4$. So now we have $\sqrt{4}$.

Step3: Evaluate the square root

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

Answer:

2