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JAMB Mathematics 2015 Paper

Question : 60

Total: 61

Rationalize 5 ÷ (2 − √3)

Solution:

Concept:

Rationalizing a denominator means removing the square root by multiplying with the conjugate.

Explanation:

The conjugate of

2 - \sqrt{3}

2 + \sqrt{3}

Multiply the original expression by

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

, which is equal to

1

\frac{5}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}}

This becomes:

\frac{5(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})}

Simplify the denominator using the difference of two squares:

(2 - \sqrt{3})(2 + \sqrt{3}) = (2)^2 - (\sqrt{3})^2

= 4 - 3 = 1

So the expression simplifies to:

\frac{5(2 + \sqrt{3})}{1} = 5(2 + \sqrt{3})

Answer:

5(2 + \sqrt{3})

, which is option C.

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