(≤ft({3{6}+{54}}{{5}(3{5})})^{-1}

Correct Answer is : 5612{5{6}}{12}1256

Correct Answer is : 5612{5{6}}{12}1256

Test Index

WAEC Further Mathematics 2022 Paper

Question : 2

Total: 45

(

\left(\frac{3\sqrt{6}+\sqrt{54}}{\sqrt{5}(3\sqrt{5})}\right)^{-1}

Solution:

Concept:

Simplify the surds inside the bracket, then use the negative index to take the reciprocal.

Explanation:

First simplify

\sqrt{54}

\sqrt{54} = \sqrt{9 \times 6} = 3\sqrt{6}

So the numerator becomes:

3\sqrt{6} + \sqrt{54} = 3\sqrt{6} + 3\sqrt{6} = 6\sqrt{6}

The denominator is:

\sqrt{5}(3\sqrt{5}) = 3 \times 5 = 15

Therefore, the bracket simplifies to:

\frac{6\sqrt{6}}{15} = \frac{2\sqrt{6}}{5}

Applying the power

-1

gives the reciprocal:

\left(\frac{2\sqrt{6}}{5}\right)^{-1} = \frac{5}{2\sqrt{6}}

Rationalize the denominator:

\frac{5}{2\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{5\sqrt{6}}{12}

Answer:

\frac{5\sqrt{6}}{12}

, which is Option C.

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