Find an irrational number between \( \begin{array}{lll}\text { (1) } 2 \text { and } 3 & \text { (2) } & \sqrt{2} \text { and } \sqrt{3} \\ \text { (3) }\end{array} \) and \( 2 \pi \)
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Bonus Knowledge
A fun and sneaky way to find an irrational number between 2 and 3 is to look at the square root of a non-perfect square! For example, \( \sqrt{5} \) fits perfectly because it's approximately 2.236, which snugly sits between the two whole numbers. Now, when searching between \( \sqrt{2} \) and \( \sqrt{3} \), \( \sqrt{2.5} \) can be your go-to! It's around 1.58, making it an exciting option as it smoothly dances between those square roots. Lastly, for a choice between 2 and \( 2\pi \) (approximately 6.28), there are plenty of choices like \( \frac{7}{3} \), which equals approximately 2.33, concocting a lovely spot to hang out in this range.