We are asked to evaluate four expressions involving square roots: e) $\sqrt{2} \times \sqrt{6}$ f) $\sqrt{\frac{9}{5}} \sqrt{\frac{2}{3}}$ g) $\sqrt{\frac{15}{5}}$ h) $\sqrt{\frac{28}{7}}$

1. Problem Description

We are asked to evaluate four expressions involving square roots:

e) $\sqrt{2} \times \sqrt{6}$

f) $\sqrt{\frac{9}{5}} \sqrt{\frac{2}{3}}$

g) $\sqrt{\frac{15}{5}}$

h) $\sqrt{\frac{28}{7}}$

2. Solution Steps

e) $\sqrt{2} \times \sqrt{6}$

$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$

$\sqrt{2} \times \sqrt{6} = \sqrt{2 \times 6} = \sqrt{12}$

$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$

f) $\sqrt{\frac{9}{5}} \sqrt{\frac{2}{3}}$

$\sqrt{\frac{9}{5}} \sqrt{\frac{2}{3}} = \sqrt{\frac{9}{5} \times \frac{2}{3}}$

$\sqrt{\frac{9 \times 2}{5 \times 3}} = \sqrt{\frac{18}{15}} = \sqrt{\frac{6}{5}}$

$\sqrt{\frac{6}{5}} = \frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{6} \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}} = \frac{\sqrt{30}}{5}$

g) $\sqrt{\frac{15}{5}}$

$\sqrt{\frac{15}{5}} = \sqrt{3}$

h) $\sqrt{\frac{28}{7}}$

$\sqrt{\frac{28}{7}} = \sqrt{4} = 2$

3. Final Answer

e) $2\sqrt{3}$

f) $\frac{\sqrt{30}}{5}$

g) $\sqrt{3}$

h) $2$