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Irrational numbers: cheat sheet

Irrational numbers and index laws · The words and methods from the lessons, with an example of each.

rational and irrational

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

rational: abirrational: 2, π\text{rational: } \tfrac{a}{b} \qquad \text{irrational: } \sqrt{2},\ \pi
A number line to zoom in on √2
A number line to zoom in on √2

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⇒5<30<625 < 30 < 36 \Rightarrow 5 < \sqrt{30} < 6