Rationalize {2{3} + {5}}{{5} - {3}}

Correct Answer is : (3 √ 15 +11) / 2

Correct Answer is : (3 √ 15 +11) / 2

Test Index

JAMB Mathematics 2010 Paper

Question : 2

Total: 49

Rationalize

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

Solution:

Concept:

To rationalize a denominator containing surds, multiply the numerator and denominator by the conjugate of the denominator.

Explanation:

The conjugate of

\sqrt{5} - \sqrt{3}

\sqrt{5} + \sqrt{3}

Multiply the expression by

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

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

Expand the numerator:

(2\sqrt{3} + \sqrt{5})(\sqrt{5} + \sqrt{3}) = 2\sqrt{15} + 6 + 5 + \sqrt{15}

= 3\sqrt{15} + 11

Simplify the denominator:

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

Therefore, the rationalized form is:

\frac{3\sqrt{15} + 11}{2}

Answer:

\frac{3\sqrt{15} + 11}{2}

This corresponds to option A.

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