Multiplying and Dividing Square Roots

Feedback: Not quite! We used the multiplication rule for square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. We break $50$ into $25 \times 2$, so $\sqrt{50} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$.

Feedback: Not quite! We used the multiplication rule for square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. We broke 72 into $36 \times 2$. So, $\sqrt{72} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$.

Feedback: Not quite! We used the division rule for square roots, which states $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. So, $\frac{\sqrt{50}}{\sqrt{2}} = \sqrt{\frac{50}{2}} = \sqrt{25} = 5$.

Feedback: Not quite! We used the division rule for square roots, which states $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. So, $\frac{\sqrt{36}}{\sqrt{9}} = \sqrt{\frac{36}{9}} = \sqrt{4} = 2$.

Feedback: Not quite! We use the division rule for square roots, which states $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. So, $\sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5}$.

Feedback: Not quite! We use the rule $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$. So, $ \sqrt{0.63} \times \sqrt{100} = \sqrt{0.63 \times 100} = \sqrt{63}$. Now, rewrite $\sqrt{63}$ as $\sqrt{9 \times 7}$, simplifying $\sqrt{9}$ as $3$, we get the result: 3 \times \sqrt{7}$.