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JAMB Mathematics 2013 Paper

Question : 7

Total: 47

Simplify

\frac{\sqrt{5}(\sqrt{147}-\sqrt{12})}{\sqrt{15}}

Solution:

Concept:

Simplify surds by factoring each number under the square root into perfect squares, then cancel common factors.

Explanation:

Write

147 = 49 \times 3

and

12 = 4 \times 3

\sqrt{147} = 7\sqrt{3}

and

\sqrt{12} = 2\sqrt{3}

The bracket becomes

7\sqrt{3} - 2\sqrt{3} = 5\sqrt{3}

Also rewrite the denominator as

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

Substitute these into the original expression:

\frac{\sqrt{5}(\sqrt{147}-\sqrt{12})}{\sqrt{15}} = \frac{\sqrt{5}(5\sqrt{3})}{\sqrt{5}\sqrt{3}}

Cancel

\sqrt{5}

and

\sqrt{3}

from the numerator and denominator.

The result is

5

Answer:

5

(Option A).

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