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Indices and Surds. Here b is called the Index. This means a to the power of b . . This gives us our first rule of indices. This gives us our second rule of indices. Page 112 Exercise 1 Page 113 Exercise 2. This gives us our third rule of indices. Page 113 Exercise 3. Harder Examples.

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Here b is called the Index

This means a to the power of b.

This gives us our first rule of indices

This gives us our second rule of indices


Page 112 Exercise 1

Page 113 Exercise 2

harder examples
Harder Examples

Page 114 Exercise 4B

fractional indices
Fractional Indices

This gives us rule 6:


= 4


Page 116 117 Exercise 6A and 6B



Irrational Numbers: Numbers that can not be written as a fraction.

A surd is a special irrational number. It is a square root, cube root, etc. that can not be expressed as a rational number.


Page 121 Exercise 8A

Page 122 Exercise 8B Up to and including Question 7

Page 123 Check up Exercise

rationalising a surd denominator
Rationalising a Surd Denominator

A surd is an irrational number

If we have a surd as a denominator we should attempt to rationalise the denominator by removing the surd. i.e. make the denominator into a rational number.

What is the only number we can multiply by and not change the value of the number we start with?

The answer of course is 1.

Remember we can write the number one in many different ways.


Things get a little more complicated when we get a fraction like

Here we have to remember the properties of a difference of two squares.

So we end up with a whole number.