Introduction To Surds
A surd is a root of a number. Often the number inside the root cannot be rooted Eg. root5. A surd can have any power with it. You can rationalise or simlify surds in many ways. Often they are used to show a more exact reading of an irrational number.
Like And Unlike Surds
Like surds have the same irrational factor. They can be added and taken away from each other.
Eg. 4root5 + 5root5 + 9root5
Unlike surds cannot do this
Equations And Inequations
Equations and inequations should be structured in exactly the same way whether they include surds or not. They can be sorted in the same mannor.
A few things to remember:
- a surd multiplies by the same surd equals the number inside the surds. Eg. root5 x root5 = 5
- roota + rootb DOES NOT equal roota+b
- roota x rootb DOES equal rootab
Rationalising The Denominator
To rationationalise a denominator (this is to say making the bottom number of a fraction a rational interger) you must multily the whole fraction by what is on the bottom.
Eg. if there is 2 over 4root5 you must multiple both top and bottom by 4root5.
If there is more than one factor on the bottom of the eqution then you must multily it by the same factors but with the signs switched, in order to make this work.This will be the same as the difference of two squares.
Eg. if you have 2 over 4root5 + 7 you must muliply top and bottom by 4root5 - 7.