# Roots

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Irrational numbers cannot be written as exact decimals or fractions. Surds are irrational numbers that can be represented as square/cube roots i.e. in surd form.

Only surds with the same number inside the square roots can be added together or subtracted from each other. For example, 2β3 + 4β3 = 6β3.

When multiplying surds, find the product of the numbers outside the root and then the product of the numbers under the roots. If the same number is under the roots, the product will be a whole number.

The division of surds should be completed by components β first divide the whole numbers, then divide the numbers under the roots.

In many calculations involving surds, the final number under the root can be simplified using the division and multiplication rules. The number under the root should be as small as possible.

To simplify a fraction with a surd in the denominator, multiply the top and bottom by the surd to rationalise the denominator.

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