253. Extract the root: а) $\sqrt{4 \cdot 9}$; б) $\sqrt{\frac{49}{36}}$; в) $\sqrt[3]{a^{6}}$; г) $\sqrt{9 a^{2}}$.
Solution. a) According to rule I, $\sqrt{4 \cdot 9}=\sqrt{4} \cdot \sqrt{9}=2 \cdot 3=6$.

b) Using rule II, we find $\sqrt{\frac{49}{36}}=\frac{\sqrt{49}}{\sqrt{36}}=\frac{7}{6}$.

c) By rule III, $\sqrt[3]{a^{6}}=a^{2}$.

d) According to rules I, III, $\sqrt{9 a^{2}}=\sqrt{9} \cdot \sqrt{a^{2}}=3 a$. 254-257. Extract the root from the product: