Simplify {1 - 2{5}}{2 + 3{2}}.

Correct Answer is : 114(32+45−610−2)1/14(3{2} + 4{5} - 6{10} - 2)141(32+45−610−2)

Correct Answer is : 114(32+45−610−2)1/14(3{2} + 4{5} - 6{10} - 2)141(32+45−610−2)

Test Index

WAEC Further Mathematics 2015 Paper

Question : 1

Total: 40

Simplify

\frac{1 - 2\sqrt{5}}{2 + 3\sqrt{2}}

Solution:

Concept:

Rationalise the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.

Explanation:

The conjugate of

2 + 3\sqrt{2}

2 - 3\sqrt{2}

Multiply the given fraction by

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

\frac{1 - 2\sqrt{5}}{2 + 3\sqrt{2}} \times \frac{2 - 3\sqrt{2}}{2 - 3\sqrt{2}}

Simplify the numerator:

= \frac{2 - 3\sqrt{2} - 4\sqrt{5} + 6\sqrt{10}}{4 - 18}

= \frac{2 - 3\sqrt{2} - 4\sqrt{5} + 6\sqrt{10}}{-14}

Divide each term in the numerator by

-14

= \frac{-2 + 3\sqrt{2} + 4\sqrt{5} - 6\sqrt{10}}{14}

Rearranging the terms gives:

= \frac{1}{14}(3\sqrt{2} + 4\sqrt{5} - 6\sqrt{10} - 2)

Answer:

Option C:

\frac{1}{14}(3\sqrt{2} + 4\sqrt{5} - 6\sqrt{10} - 2)

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