Let’s work through each question one by one:

Q7: Simplify the square root

1. $\sqrt{\frac{147}{8}}$

1. Factor the numerator and denominator inside the square root: $\frac{147}{8} = \frac{49 \times 3}{4 \times 2}$

2. Separate into two square roots: $\sqrt{\frac{147}{8}} = \frac{\sqrt{147}}{\sqrt{8}}$

3. Simplify each part:

   • $\sqrt{147} = \sqrt{49 \times 3} = 7\sqrt{3}$
   • $\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$

4. Combine to get the simplified form: $\frac{7\sqrt{3}}{2\sqrt{2}}$

5. Rationalize the denominator by multiplying numerator and denominator by $\sqrt{2}$: $= \frac{7\sqrt{6}}{4}$

2. $\sqrt{\frac{282}{3}}$

1. Factor the numbers inside the square root: $\frac{282}{3} = 94$
2. Take the square root: [ \sqrt