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WAEC Mathematics 2022 Paper

Question : 4

Total: 47

If √24 + √96 - √600 = y√6, find the value of y

Solution:

Concept:

Simplify each surd by expressing it as a multiple of

\sqrt{6}

, then combine like terms.

Explanation:

First, rewrite each square root in surd form.

\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}

\sqrt{96} = \sqrt{16 \times 6} = 4\sqrt{6}

\sqrt{600} = \sqrt{100 \times 6} = 10\sqrt{6}

Now substitute these into the given expression.

2\sqrt{6} + 4\sqrt{6} - 10\sqrt{6} = (2 + 4 - 10)\sqrt{6}

(2 + 4 - 10)\sqrt{6} = -4\sqrt{6}

This is equal to

y\sqrt{6}

, so comparing the coefficients gives

y = -4

Answer:

y = -4

Option D.

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