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WAEC Mathematics 2013 Paper

Question : 6

Total: 48

\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}

, find K

Solution:

Concept:

Rewrite every surd in the equation as a multiple of

\sqrt{2}

, then isolate

K

Explanation:

Start with the given equation:

\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}

Simplify each term.

\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}

\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}

\frac{2}{\sqrt{2}} = \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \sqrt{2}

Substitute the simplified terms back into the equation:

5\sqrt{2} - K(2\sqrt{2}) = \sqrt{2}

Factor out

\sqrt{2}

from the left-hand side:

\sqrt{2}(5 - 2K) = \sqrt{2}

Divide both sides by

\sqrt{2}

5 - 2K = 1

Subtract 5 from both sides:

-2K = -4

Divide both sides by

-2

K = 2

Answer:

K = 2

, so the correct option is D.

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