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JAMB Mathematics 2019 Paper

Question : 63

Total: 73

\sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175}

Solution:

Concept:

Simplify each surd by expressing it in terms of

\sqrt{7}

, then solve for

k

Explanation:

Start with the equation:

\sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175}

Rewrite each square root using perfect square factors:

\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}

\sqrt{112} = \sqrt{16 \times 7} = 4\sqrt{7}

\sqrt{175} = \sqrt{25 \times 7} = 5\sqrt{7}

Substitute these into the equation:

2\sqrt{7} + 4\sqrt{7} - \sqrt{k} = 5\sqrt{7}

Combine the like surds on the left:

6\sqrt{7} - \sqrt{k} = 5\sqrt{7}

Rearrange to isolate

\sqrt{k}

6\sqrt{7} - 5\sqrt{7} = \sqrt{k}

\sqrt{7} = \sqrt{k}

Square both sides:

k = 7

Answer:

The value of

k

7

, which is option B.

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