What is the value of \(2\sqrt{5}\times 3\sqrt{5}\)?
Answer and explanation
Correct answer: 30
\(2\sqrt{5}\times 3\sqrt{5}=(2\times3)\times(\sqrt{5}\times\sqrt{5})=6\times5=30\). Multiplying like radicals uses \(\sqrt{a}\cdot\sqrt{a}=a\), so the product is rational. The nearest distractor, \(6\sqrt{5}\), arises from multiplying coefficients only and forgetting to simplify the radical part. Exam tip: for products of the form \((a\sqrt{b})(c\sqrt{b})\), compute \(ac\) and use \(\sqrt{b}\cdot\sqrt{b}=b\) to simplify.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
\(2\sqrt{5}\times 3\sqrt{5}=(2\times3)\times(\sqrt{5}\times\sqrt{5})=6\times5=30\). Multiplying like radicals uses \(\sqrt{a}\cdot\sqrt{a}=a\), so the product is rational. The nearest distractor, \(6\sqrt{5}\), arises from multiplying coefficients only and forgetting to simplify the radical part. Exam tip: for products of the form \((a\sqrt{b})(c\sqrt{b})\), compute \(ac\) and use \(\sqrt{b}\cdot\sqrt{b}=b\) to simplify.
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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