High School

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Pete had to simplify the following expression on his math test:

\[
\frac{\sqrt{2} \cdot \sqrt{2}}{3\sqrt{2} \cdot \sqrt{5}}
\]

Pete said the answer is \(\frac{2}{3\sqrt{10}}\) but his teacher marked it as incorrect.

What was Pete’s mistake? Explain to Pete how he can fix his mistake.

Answer :

Pete's mistake was to skip reducing the fraction to the lowest possible terms.

Here's how Pete can fix the mistake:

[tex]\frac{\sqrt{2}\sqrt{2}}{3\sqrt{2}\sqrt{5}}= \frac{\sqrt{2}}{3\sqrt{5}}=\sqrt{\frac{2}{9\cdot5}}=\sqrt{\frac{2}{45}}[/tex]

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