Question

Answer 1

1) \(\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=\dfrac{\sqrt{2}}{2}\)

2) \(\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{\sqrt{3}\cdot\sqrt{3}}=\dfrac{\sqrt{3}}{3}\)

3) \(\dfrac{1}{\sqrt{5}}=\dfrac{\sqrt{5}}{\sqrt{5}\cdot\sqrt{5}}=\dfrac{\sqrt{5}}{5}\)

4) \(\dfrac{1}{\sqrt{7}}=\dfrac{\sqrt{7}}{\sqrt{7}\cdot\sqrt{7}}=\dfrac{\sqrt{7}}{7}\)

5) \(\dfrac{3}{\sqrt{3}}=\dfrac{\sqrt{3}\cdot\sqrt{3}}{\sqrt{3}}=\sqrt{3}\)

6) \(\dfrac{12}{5\sqrt{3}}=\dfrac{12\cdot\sqrt{3}}{5\sqrt{3}\cdot\sqrt{3}}=\dfrac{12\sqrt{3}}{5\cdot3}=\dfrac{12\sqrt{3}}{15}=\dfrac{4\sqrt{3}}{5}\)

7) \(\dfrac{14}{\sqrt{7}}=\dfrac{\sqrt{7}\cdot\sqrt{7}\cdot2}{\sqrt{7}}=\sqrt{7}\cdot2=2\sqrt{7}\)

8) \(\dfrac{\sqrt{3}}{\sqrt{2}}=\dfrac{\sqrt{3}\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=\dfrac{\sqrt{6}}{2}\)

9) \(\dfrac{5}{\sqrt{10}}=\dfrac{\sqrt{5}\cdot\sqrt{5}\cdot\sqrt{2}}{\sqrt{5}\cdot\sqrt{2}\cdot\sqrt{2}}=\dfrac{\sqrt{10}}{2}\)

10) \(\dfrac{3}{2\sqrt{5}}=\dfrac{3\cdot\sqrt{5}}{2\sqrt{5}\cdot\sqrt{5}}=\dfrac{3\sqrt{5}}{10}\)