Indices and Surds

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Indices and Surds
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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
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Page 112 Exercise 1 Page 113 Exercise 2
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This gives us our third rule of indices
Page 113 Exercise 3
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Harder Examples
Page 114 Exercise 4B
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Zero and negative indices
Rule 4
Rule 5
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Page 115 Exercise 5A and 5B
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Fractional Indices
This gives us rule 6
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Revision
Page 116 117 Exercise 6A and 6B
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Surds
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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.
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When simplifying a surd always look for a square
number as a factor.
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Page 121 Exercise 8A
Page 122 Exercise 8B Up to and including
Question 7
Page 123 Check up Exercise
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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.
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This is a fraction with a rational denominator.
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This is a fraction with a rational denominator.
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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.
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