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AQA GCSE Maths Roots

Roots

This page covers the following topics:

1. Surds
2. Addition and subtraction of roots
3. Multiplication of surds
4. Division of surds
5. Simplifying surds

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.

Surds

Only surds with the same number inside the square roots can be added together or subtracted from each other, unless it is possible to simplify the different roots to the same one. For example, 2√3 + 4√3 = 6√3.

Addition and subtraction of roots

To 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 of such roots is a whole number.

Multiplication of surds

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

Division of surds

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.

Simplifying surds

1

Fully simplify √5(√125 βˆ’ √5).

Fully simplify √5(√125 βˆ’ √5).

2

Simplify 9√3 Γ— 4√3.

Simplify 9√3 Γ— 4√3.

3

Simplify (8√6)/(2√4).

Simplify (8√6)/(2√4).

4

Simplify √3 Γ— √7, leave your answer in surd form.

Simplify √3 Γ— √7, leave your answer in surd form.

5

Simplify 6√10 + 3√2 βˆ’ √10, if possible.

Simplify 6√10 + 3√2 βˆ’ √10, if possible.

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