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WAEC Mathematics 2020 Paper

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Question : 7

Total: 48

Given that

\frac{\sqrt{3}+\sqrt{5}}{\sqrt{5}}

1 $\frac{3}{5}$
1 $\frac{2}{5}$
1 $\frac{1}{5}$
$\frac{1}{5}$

Solution:

Concept:

The given surd expression can be written in the form

x + y\sqrt{15}

. Compare the rational and irrational parts after multiplying by

\sqrt{5}

.

Explanation:

Let

\frac{\sqrt{3}+\sqrt{5}}{\sqrt{5}} = x + y\sqrt{15}

.

Multiply both sides by

\sqrt{5}

:

\sqrt{3} + \sqrt{5} = x\sqrt{5} + y\sqrt{15}\sqrt{5}

.

Since

\sqrt{15}\sqrt{5} = \sqrt{75} = 5\sqrt{3}

, we get:

\sqrt{3} + \sqrt{5} = x\sqrt{5} + 5y\sqrt{3}

.

Compare the

\sqrt{5}

terms:

x\sqrt{5} = \sqrt{5}

, so

x = 1

.

Compare the

\sqrt{3}

terms:

5y\sqrt{3} = \sqrt{3}

, so

5y = 1

, giving

y = \frac{1}{5}

.

Therefore,

x + y = 1 + \frac{1}{5} = \frac{6}{5} = 1\frac{1}{5}

.

Answer:

1\frac{1}{5}

Option C.

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