Question

Pete had to simplify the following expression on his math test. (√2 ∙ √2)/(3√2 ∙ √5) Pete said the answer is 2/(3√10 ) but his teacher marked it as incorrect. What was Pete’s mistake? Explain to Pete how he can fix his mistake.

Answer 1

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

Here's how Pete can fix the mistake:

$\frac{\sqrt{2}\sqrt{2}}{3\sqrt{2}\sqrt{5}}= \frac{\sqrt{2}}{3\sqrt{5}}=\sqrt{\frac{2}{9\cdot5}}=\sqrt{\frac{2}{45}}$