Simplify $\frac{\sqrt{5}(\sqrt{147} - \sqrt{12}}{\sqrt{15}}$

Analyze the question: We need to simplify √5(√147 − √12) / √15.

Concept: Simplify each surd by pulling out perfect squares, then cancel common factors.

Solution:

1. Simplify the surds: • √147 = √(49 × 3) = 7√3 • √12 = √(4 × 3) = 2√3

2. Subtract: √147 − √12 = 7√3 − 2√3 = 5√3

3. Multiply by √5 in the numerator: √5 × 5√3 = 5√15

4. Divide by √15: 5√15 / √15 = 5

Check against the options: The result is 5, which matches option A.

Tip: In surd questions, first reduce each surd to its simplest form (look for 4, 9, 25, 49 as factors). Like surds (such as 7√3 and 2√3) can then be added or subtracted just like like terms in algebra. Often the surd cancels completely at the end, which is a good sign that you are on track.