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Find three rational numbers between 2/5 and 3/5.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Find three rational numbers between $\dfrac{2}{5}$ and $\dfrac{3}{5}$ .

Need a reminder? The key ideaShow

Every real number is a point on the number line. Between any two numbers there are infinitely many rational numbers, such as their average. The square root spiral builds $\sqrt{2}$ , $\sqrt{3}$ , $\sqrt{4}$ and so on, one triangle at a time.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← Show that √5 is irrational. Why does the same argument fail for √9?In the square root spiral, the first triangle has two sides of 1, and each new triangle has one… →

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