Simplify: {108} + {125} - {75}

Correct Answer is : 3+55{3} + 5{5}3+55

Correct Answer is : 3+55{3} + 5{5}3+55

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WAEC Mathematics 2018 Paper

Question : 1

Total: 50

Simplify:

\sqrt{108} + \sqrt{125} - \sqrt{75}

Solution:

Concept:

Simplify each radical by extracting perfect square factors, then combine like terms.

Explanation:

Write each term as a product of a perfect square and a remaining factor.

\sqrt{108} = \sqrt{36 \times 3} = 6\sqrt{3}

\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}

\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}

Now substitute back into the expression:

6\sqrt{3} + 5\sqrt{5} - 5\sqrt{3}

Combine the like terms involving

\sqrt{3}

6\sqrt{3} - 5\sqrt{3} = \sqrt{3}

So the expression becomes

\sqrt{3} + 5\sqrt{5}

Answer:

\sqrt{3} + 5\sqrt{5}

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