what is the following quotient?\n$\frac{sqrt{120}}{sqrt{30}}$\n2\n4\n$2sqrt{10}$\n$3sqrt{10}$
what is the following quotient?\n$\frac{sqrt{120}}{sqrt{30}}$\n2\n4\n$2sqrt{10}$\n$3sqrt{10}$
Answer
Explanation:
Step1: Use quotient - rule of square roots
The quotient - rule of square roots states that $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$ for $a\geq0$ and $b > 0$. Here, $a = 120$ and $b = 30$, so $\frac{\sqrt{120}}{\sqrt{30}}=\sqrt{\frac{120}{30}}$.
Step2: Simplify the fraction inside the square root
Calculate $\frac{120}{30}=4$. So, $\sqrt{\frac{120}{30}}=\sqrt{4}$.
Step3: Evaluate the square root
Since $\sqrt{4} = 2$, the quotient is 2.
Answer:
A. 2