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WAEC Mathematics 2012 Paper

Question : 2

Total: 49

Simplify;

\; \frac{3\sqrt{5} \; \times \; 4\sqrt{6}}{2 \; \sqrt{3} \times 3\sqrt{2}}

Solution:

Concept:

Simplify the surds by multiplying numerators and denominators separately, then cancel common factors.

Explanation:

Multiply the coefficients and surds in the numerator:

3\sqrt{5} \times 4\sqrt{6} = 12\sqrt{30}

Multiply the coefficients and surds in the denominator:

2\sqrt{3} \times 3\sqrt{2} = 6\sqrt{6}

Form the fraction:

\frac{12\sqrt{30}}{6\sqrt{6}} = 2\frac{\sqrt{30}}{\sqrt{6}}

Simplify the surd quotient:

\frac{\sqrt{30}}{\sqrt{6}} = \sqrt{\frac{30}{6}} = \sqrt{5}

Therefore:

2\sqrt{5}

Answer:

2\sqrt{5}

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