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WAEC Mathematics 2016 Paper

Question : 3

Total: 49

Simplify:(

\;\frac{10\sqrt{3}}{\sqrt{5}} - \sqrt{15}

)²

Solution:

Concept:

Rationalise the denominator and simplify the expression before squaring.

Explanation:

Start with the fraction

\frac{10\sqrt{3}}{\sqrt{5}}

Multiply numerator and denominator by

\sqrt{5}

\frac{10\sqrt{3}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{10\sqrt{15}}{5}

Simplify:

\frac{10\sqrt{15}}{5} = 2\sqrt{15}

Now substitute into the given expression:

\left(\frac{10\sqrt{3}}{\sqrt{5}} - \sqrt{15}\right)^2 = (2\sqrt{15} - \sqrt{15})^2

Combine like terms:

2\sqrt{15} - \sqrt{15} = \sqrt{15}

Square the result:

(\sqrt{15})^2 = 15

Therefore, the simplified value is

15.00

Answer:

Option B:

15.00

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