Simplify; {{5}+3}{4-{10}}

Correct Answer is : 232/3325{5}5 + 5625/6{2}652 + 12101/2{10}2110 + 2

Correct Answer is : 232/3325{5}5 + 5625/6{2}652 + 12101/2{10}2110 + 2

Test Index

WAEC Further Mathematics 2020 Paper

Question : 7

Total: 39

Simplify;

\frac{\sqrt{5}+3}{4-\sqrt{10}}

Solution:

Concept:

Rationalise the denominator by multiplying by the conjugate, then simplify each term.

Explanation:

Multiply numerator and denominator by

4+\sqrt{10}

\frac{\sqrt{5}+3}{4-\sqrt{10}} \times \frac{4+\sqrt{10}}{4+\sqrt{10}}

The denominator becomes:

(4-\sqrt{10})(4+\sqrt{10})=16-10=6

The numerator expands as:

(\sqrt{5}+3)(4+\sqrt{10})=4\sqrt{5}+\sqrt{50}+12+3\sqrt{10}

Since

\sqrt{50}=5\sqrt{2}

, the expression is:

\frac{4\sqrt{5}+5\sqrt{2}+12+3\sqrt{10}}{6}

Divide each term by 6:

\frac{2}{3}\sqrt{5}+\frac{5}{6}\sqrt{2}+2+\frac{1}{2}\sqrt{10}

This is option C.

Answer:

\frac{2}{3}\sqrt{5}+\frac{5}{6}\sqrt{2}+\frac{1}{2}\sqrt{10}+2

Option C.

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