What is the value of (\sqrt{45}-\sqrt{20})? Give the answer in simplified form.
Answer and explanation
Correct answer: \sqrt{5}
\sqrt{45}=\sqrt{9\cdot5}=3\sqrt{5} and \sqrt{20}=\sqrt{4\cdot5}=2\sqrt{5}. Subtracting gives 3\sqrt{5}-2\sqrt{5}=\sqrt{5}. The closest distractor D (2\sqrt{5}) is incorrect because it equals \sqrt{20}, not the difference. Exam tip: factor common square factors (like \sqrt{5}) to simplify radicals before adding or subtracting.
Frequently asked questions
What is the correct answer to this question?
\sqrt{5}
Why is this the correct answer?
\sqrt{45}=\sqrt{9\cdot5}=3\sqrt{5} and \sqrt{20}=\sqrt{4\cdot5}=2\sqrt{5}. Subtracting gives 3\sqrt{5}-2\sqrt{5}=\sqrt{5}. The closest distractor D (2\sqrt{5}) is incorrect because it equals \sqrt{20}, not the difference. Exam tip: factor common square factors (like \sqrt{5}) to simplify radicals before adding or subtracting.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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