JAMB 2013 · UTME · Q8

Simplify $\dfrac{\sqrt5(\sqrt{147} - \sqrt{12})}{\sqrt{15}}$ .

Worked solution (try it first)

Take out square factors: $\sqrt{147} = 7\sqrt3$ and $\sqrt{12} = 2\sqrt3$ , so the bracket is $5\sqrt3$ .
Multiply by $\sqrt5$ : $5\sqrt3 \times \sqrt5 = 5\sqrt{15}$ .
Divide by $\sqrt{15}$ : $\dfrac{5\sqrt{15}}{\sqrt{15}} = 5$ , option C.