EasyMathematicsHigh School (9–10)GeneralNumber Systems › Rational and Irrational Numbers Number Systems › Exponents and RadicalsConceptual

Say whether each number is rational or irrational.

Contributed by StemPy Lab

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

$4 - \sqrt{5}$

$2\sqrt{7}$

$\sqrt{3} \times \sqrt{27}$

$(\sqrt{7} + \sqrt{2})(\sqrt{7} - \sqrt{2})$

$\dfrac{\sqrt{50}}{\sqrt{2}}$

$(\sqrt{3})^3$

Need a reminder? The key ideaShow

Rational plus irrational is irrational, while two irrational numbers can give either kind. $\sqrt{a}\,\sqrt{b} = \sqrt{ab}$ , but $\sqrt{a} + \sqrt{b} \neq \sqrt{a + b}$ . $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = a - b$ and $(\sqrt{a} + \sqrt{b})^2 = a + b + 2\sqrt{ab}$ .

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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