Multiplying and Dividing Square Roots

We use the multiplication rule for square roots: $\sqrt{a\times b}=\sqrt{a}\times \sqrt{b}$. We break 50 into $25\times 2$, so $\sqrt{50}=\sqrt{25}\times \sqrt{2}=5\sqrt{2}$.

We use the multiplication rule for square roots: $\sqrt{a\times b}=\sqrt{a}\times \sqrt{b}$. We break 72 into $36\times 2$, so $\sqrt{72}=\sqrt{36}\times \sqrt{2}=6\sqrt{2}$.

We use the division rule for square roots, which states $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$. So, $\frac{\sqrt{50}}{\sqrt{2}}=\sqrt{\frac{50}{2}}=\sqrt{25}=5$.

We use the division rule for square roots, which states $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$. So, $\frac{\sqrt{36}}{\sqrt{9}}=\sqrt{\frac{36}{9}}=\sqrt{4}=2$.

We use the division rule for square roots, which states $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$. So, $\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\frac{4}{5}$.

We use the rule $\sqrt{a}\times \sqrt{b}=\sqrt{a\times b}$. So, $\sqrt{0.63}\times \sqrt{100}=\sqrt{63}$. Now rewrite $\sqrt{63}$ as $\sqrt{9\times 7}$, simplifying $\sqrt{9}$ as 3, we get the result $3\sqrt{7}$.