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Let’s work through each question one by one:

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### 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

Simplify the square root and factor expressions (Q7 to Q10).

Learn how to simplify square roots, factor quadratic expressions using the AC method, and solve quadratic equations using the quadratic formula. These problems cover algebraic concepts essential for students in Grades 9-11.

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