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

Correct Answer is : 1−54{1 - {5}}{4}41−5

Correct Answer is : 1−54{1 - {5}}{4}41−5

Test Index

JAMB Mathematics 2011 Paper

Question : 7

Total: 46

Rationalize

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

Solution:

Concept:

Rationalizing a denominator removes the radical from the denominator by multiplying with its conjugate.

Explanation:

Multiply the numerator and denominator by the conjugate of

3 - \sqrt{5}

, which is

3 + \sqrt{5}

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

Expand the numerator:

(2 - \sqrt{5})(3 + \sqrt{5}) = 6 + 2\sqrt{5} - 3\sqrt{5} - 5 = 1 - \sqrt{5}

Expand the denominator:

(3 - \sqrt{5})(3 + \sqrt{5}) = 9 - 5 = 4

So the expression becomes:

\frac{1 - \sqrt{5}}{4}

Answer:

\frac{1 - \sqrt{5}}{4}

This is Option B.

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