Evaluate: {75}+{18}-{27}

Correct Answer is : 23+32\;\;2{3}+3{2}23+32

Correct Answer is : 23+32\;\;2{3}+3{2}23+32

Test Index

BECE Mathematics 2024 Paper

Question : 11

Total: 40

Evaluate:

\sqrt{75}+\sqrt{18}-\sqrt{27}

Solution:

Concept:

Simplify each surd by expressing the number under the root as a product of a perfect square and another number.

Explanation:

First, factorise each term:

75 = 25 \times 3

18 = 9 \times 2

, and

27 = 9 \times 3

Use

\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}

So,

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

\sqrt{18} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}

\sqrt{27} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}

Now substitute:

5\sqrt{3} + 3\sqrt{2} - 3\sqrt{3}

Combine like surds:

5\sqrt{3} - 3\sqrt{3} = 2\sqrt{3}

Thus, the expression simplifies to

2\sqrt{3} + 3\sqrt{2}

Answer:

2\sqrt{3} + 3\sqrt{2}

, which is option B.

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