# Indices

Indices are sometimes called powers or exponents. For example, if y = 42

then 4 is the base and the power, or index, is 2. ## Laws of Indices

Indices obey laws :-

Rule 1 Example Rule 2 Example Rule 3 Example Rule 4 Example Rule 5 Example ## You cannot mix bases ## Manipulating indices

Examples    ## Remember      ## Surds

A surd is an expression involving unresolved roots of numbers. To simplify surds, split the number into factors involving square numbers.

Examples  ## Rules for surds

Rule 1 Example Rule 2 Example Rule 3 Example Rule 4 Example Rule 5 This is called rationalizing surds ,

the bottom number does not have any square roots.

Examples  Rule 6 Example ## Exact Values

Surds are useful when finding exact values.

Examples

Calculate the exact value of the side marked x in the following triangle :-  Is the following triangle a right-angled triangle ?  Calculate the exact value of the area of the following triangle.  This requires the base , x cm , to be found.   © Alexander Forrest