Simplify 2{3} - \; {6}{{3}} + \; {3}{{27}}

Correct Answer is : 133\; 1/3 {3}313

Correct Answer is : 133\; 1/3 {3}313

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WAEC Mathematics 2010 Paper

Question : 15

Total: 49

Simplify 2

\sqrt{3}

\; \frac{6}{\sqrt{3}} + \; \frac{3}{\sqrt{27}}

Solution:

Concept:

Rationalise the surd denominators to simplify the radical expression.

Explanation:

Start with:

2\sqrt{3} - \frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}

Rewrite

\sqrt{27}

\sqrt{9 \times 3} = 3\sqrt{3}

So the expression becomes:

2\sqrt{3} - \frac{6}{\sqrt{3}} + \frac{3}{3\sqrt{3}}

Simplify the last term:

\frac{3}{3\sqrt{3}} = \frac{1}{\sqrt{3}}

Rationalise

\frac{6}{\sqrt{3}}

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

Rationalise

\frac{1}{\sqrt{3}}

\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}

Now substitute back:

2\sqrt{3} - 2\sqrt{3} + \frac{\sqrt{3}}{3}

The

2\sqrt{3}

terms cancel, leaving

\frac{\sqrt{3}}{3}

Thus,

\frac{\sqrt{3}}{3} = \frac{1}{3}\sqrt{3}

Answer:

\frac{1}{3}\sqrt{3}

\;

i.e. Option B.

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