1. Roots of numbers which cannot be expressed as whole numbers are called SURDS
National 5 Maths
Surds

2. Rule 1 Surds can be manipulated algebraically.
Rule 1 Adding and Subtracting Surds if they are of equal value ie √5 and √5.

3. Rule 3 Simplifying Surds
A surd can be simplified if it has a square number factor.

4. Rule 2 Multiplying Surds
We can multiply Surds

5. Rule 4 Rationalising the denominator
If a fraction has a surd on the denominator, (the bottom of a fraction) then the denominator is irrational.
We can rationalise the denominator by multiplying the fraction top and bottom by the surd.