During a mental-arithmetic warm-up before an after-school mathematics club meeting begins each week, the leader asks members to simplify \(\sqrt{8} \times \...
Question 1 Report
During a mental-arithmetic warm-up before an after-school mathematics club meeting begins each week, the leader asks members to simplify \(\sqrt{8} \times \sqrt{18}\) without using a calculator, giving the final simplified answer as a whole number. (3)
Answer Details
When multiplying two square roots, they can be combined under a single root using \(\sqrt{a}\times\sqrt{b}=\sqrt{a\times b}\), which is often the fastest way to reach a whole-number answer.
Combining the two roots into one:
\[\sqrt{8}\times\sqrt{18}=\sqrt{8\times18}=\sqrt{144}\] [2 marks]Since \(144=12\times12\), the square root simplifies exactly to a whole number:
\[\sqrt{144}=12\] [1 mark]Multiplying the numbers under the root first, rather than converting each surd separately (\(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\), giving \(2\sqrt{2}\times3\sqrt{2}=6\times2=12\)), reaches the same whole-number result with less working, which is useful to recognise for "without a calculator" questions.
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