Rationalize {{6} - {4}}{{6} + {4}}

Correct Answer is : 5 - 2 6{6}6

Correct Answer is : 5 - 2 6{6}6

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JAMB Mathematics 2016 Paper

Question : 46

Total: 50

Rationalize

\frac{\sqrt{6} - \sqrt{4}}{\sqrt{6} + \sqrt{4}}

Solution:

Concept:

Rationalizing a denominator means multiplying numerator and denominator by the conjugate of the denominator.

Explanation:

Write

\sqrt{4}

2

Multiply by the conjugate of

\sqrt{6} + \sqrt{4}

, which is

\sqrt{6} - \sqrt{4}

\frac{\sqrt{6} - \sqrt{4}}{\sqrt{6} + \sqrt{4}} \times \frac{\sqrt{6} - \sqrt{4}}{\sqrt{6} - \sqrt{4}}

The denominator becomes

(\sqrt{6})^2 - (\sqrt{4})^2 = 6 - 4 = 2

The numerator becomes

(\sqrt{6} - \sqrt{4})^2 = 6 - 2\sqrt{24} + 4 = 10 - 4\sqrt{6}

So the expression is:

\frac{10 - 4\sqrt{6}}{2} = 5 - 2\sqrt{6}

Answer:

5 - 2\sqrt{6}

, which is option D.

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