When my students grow too dependent on their calculators, I ask them to find a number that, when multiplied by itself, gives them 2. Students quickly see that since 1² = 1 and 2² = 4, the answer has ...

A rational number can be written exactly in the form \(\frac{a}{b}\), where 𝑎 and 𝑏 are integers, while an irrational number cannot.

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Imagine being asked to pick a number from 1 to 10. You are quite likely to pick a whole number; I have never seen someone do otherwise. But you could also pick the number pi, whose decimal expansion ...