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

 

 

 

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 ?

Justify your answer.

 

 

Calculate the exact value of the area of the following triangle.

Give your answer in its simplest form.

 

This requires the base , x cm , to be found.