Indices

Indices are sometimes called powers or exponents.

1

For example, if y = 42

then 4 is the base and the power, or index, is 2. 

2

Laws of Indices

Indices obey laws :-

Rule 1
 

3

Example

4

Rule 2

 5

Example

6

 

Rule 3


 1

Example

14

 

Rule 4

15

Example

16

Rule 5
 

2

Example

18

 

Please Note that the base is always the same

You cannot mix bases

35

 

 

Manipulating indices

Examples

36

3

q1

 

q2

 

Remember

7 8 9 10 11 12

 

Surds

 

A surd is an expression involving unresolved roots of numbers.


19  

 

To simplify surds, split the number into factors involving square numbers.

 

Examples

20

21

 

Rules for surds

 

Rule 1

22

 Example

23

 

Rule 2

24

Example

25

 

Rule 3

216

Example

27

Rule 4

28

Example

29

 

Rule 5

30

This is called rationalizing surds ,

the bottom number does not have any square roots.

 

Examples

31

32

 

 Rule 6

33

 

Example

34

 

Exact Values

Surds are useful when finding exact values.

 

Examples

Calculate the exact value of the side marked x in the following triangle :-

 

1

 

38

 

Is the following triangle a right-angled triangle ?

Justify your answer.

12

 

3

 

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

Give your answer in its simplest form.

2

 

12

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

41

 

42

 

© Alexander Forrest