Question

1. simplify $sqrt{\frac{36}{81}}$. a. $-\frac{6}{9}$ b. $\frac{6}{9}$ c. $0.overline{3}$ d. $- 0.overline{6}$ 0.666066667

Explanation:

Step1: Recall square - root property

The square - root of a fraction $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ ($a\geq0,b > 0$). Here, $a = 36$ and $b = 81$. So, $\sqrt{\frac{36}{81}}=\frac{\sqrt{36}}{\sqrt{81}}$.

Step2: Calculate square - roots

We know that $\sqrt{36}=6$ (since $6\times6 = 36$) and $\sqrt{81}=9$ (since $9\times9 = 81$). Then $\frac{\sqrt{36}}{\sqrt{81}}=\frac{6}{9}$.

Answer:

B. $\frac{6}{9}$