Rationalise a Denominator

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Rationalise a Denominator
6-Nov-09
Objectives Convert a fraction with an irrational
denominator into one with a rational denominator
¾
Here is a fraction. The top is the numerator and
the bottom is the denominator
Here is a fraction with an irrational
denominator. You need to be able to make this
rational
2
What is an irrational number?
The square has an area of 9 square units and
square root of 3 i.e. v9 3
This blue square has an area of 5 square units
and the length of its sides will be the square
root of 5 i.e. v5
What is the v5?
Using a calculator the answer is 2.236067978 It
is impossible to find an exact answer.
An irrational number is a real number but you can
never exactly find its value!
3
11
7
3
2
The area of each square is written inside
In the same way as the v5 is irrational, the
square root of any prime number 2, 3, 5, 7, 11,
13, - is also an irrational number v2
1.4142135 v3 0.73205080
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We do not want irrational numbers as the
denominators of fractions. Here is an example of
how to deal with these
Times the top and bottom by the irrational number
The denominator is rational. The numerator is
irrational but this is the lesser of the two
evils!
5
Here is an example of how to deal with problems
that have a sum as the numerator
Times the top and bottom by the irrational number
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Rationalise the DENOMINATOR on each of these
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Rationalise the DENOMINATOR on each of these