---
title: "Irrational numbers: cheat sheet"
subtitle: "Irrational numbers and index laws"
---

# Irrational numbers

> The words and methods from this unit, with an example of each.

:::keep-together

**rational and irrational**: Rational numbers are fractions: their decimals stop or repeat. Irrational numbers never stop and never repeat. √16 = 4 is rational.

$$\text{rational: } \tfrac{a}{b} \qquad \text{irrational: } \sqrt{2},\ \pi$$

_A number line to zoom in on √2_

:::

:::keep-together

**placing a square root**: Find the perfect squares either side, then square decimals to get closer. A rounded value is an approximation.

$$25 < 30 < 36 \Rightarrow 5 < \sqrt{30} < 6$$

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