Question

question 34 of 41
which of the following is equivalent to the quotient below?
\\(\frac{\sqrt{60}}{\sqrt{5}}\\)

a. \\(4\sqrt{3}\\)
b. 12
c. \\(3\sqrt{2}\\)
d. \\(2\sqrt{3}\\)

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 $b>0$). Applying this to $\frac{\sqrt{60}}{\sqrt{5}}$, we get $\sqrt{\frac{60}{5}}$.

Step2: Simplify the fraction inside the square root

Simplify $\frac{60}{5}$: $\frac{60}{5} = 12$. So now we have $\sqrt{12}$.

Step3: Simplify $\sqrt{12}$

We can factor 12 as $4\times3$, and since $\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}$ (by the product rule for square roots), and $\sqrt{4}=2$, we get $2\sqrt{3}$.

Answer:

D. $2\sqrt{3}$