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WAEC Mathematics 2014 Paper

Question : 5

Total: 49

Simplify:

\sqrt{12} ( \sqrt{48} - \sqrt{3}

)

Solution:

Concept:

Simplify each square root using prime factors, combine like terms, then multiply.

Explanation:

Start with

\sqrt{12}(\sqrt{48} - \sqrt{3})

Express the square roots in simplest surd form:

\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}

\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}

Substitute these into the expression:

2\sqrt{3}(4\sqrt{3} - \sqrt{3})

Inside the bracket, combine the like surds:

(4\sqrt{3} - \sqrt{3}) = 3\sqrt{3}

Now multiply:

2\sqrt{3} \times 3\sqrt{3} = 6 \times (\sqrt{3} \times \sqrt{3}) = 6 \times 3 = 18

Answer:

18

(Option A)

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