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WAEC Further Mathematics 2017 Paper

Question : 23

Total: 40

Simplify

\;\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}}

Solution:

Concept:

Simplify the surds by expressing each square root as a product of a perfect square and a smaller radical.

Explanation:

First, simplify the numerator:

\sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2}

Next, simplify the denominator terms:

\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}

So the expression becomes

\frac{8\sqrt{2}}{4\sqrt{2} - 2\sqrt{2}}

Combine the terms in the denominator:

4\sqrt{2} - 2\sqrt{2} = 2\sqrt{2}

Now divide:

\frac{8\sqrt{2}}{2\sqrt{2}} = \frac{8}{2} = 4

Thus, the simplified value is

4

, which corresponds to option D.

Answer:

4

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