Indices and surds
Posted in Maths, Core 1Indices
An index (indices is the plural) is the power to which something is raised, for example in the expression 23 the index is 3 and 2 is referred to as the base.
Rules of indices
| Rule | Example |
|---|---|
Rational and irrational numbers
A rational number is one which can be written as either can integer or as the ratio of two integers (i.e. a fraction). For example, 2, ,
.
An irrational number is one which cannot be expressed as a fraction, for example or
these numbers do not end or have a recurring pattern.
Surds
Surds are expressions for irrational numbers, for example
Simplifying surds
To simplify a surd, such as firstly write it as the product of other integers, in this case
. This can be expressed as
. You know the square root of 9 is 3 and hence can simplify the expression further:
Examples
Simplify the following surds:
1.
2.
3.
4.
Here are the following worked solutions:
1. =
=
=
2. =
=
=
3. =
=
=
=
4. =
Rationalising the denominator
Knowing (x + y)(x - y) = x2 - y2 can be used to solve more complex surds, for example:
Simplify the following surd:
By multiplying both sides by you can rationalise the denominator (i.e. turn it into a rational number):
Using the rule mentioned above:
You can then expand the numerator to give your final answer: