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Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
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7.5 | Rationalising the Denominator |
In these revision notes for Rationalising the Denominator, we cover the following key points:
Rationalising the denominator means getting rid of roots when they are in the denominator of a fraction, especially when these roots contain surds.
We may often need the help of the eight special algebraic identities to multiply brackets containing surds. In many cases, they also allow us to rationalise the denominator of a fraction.
There exist three kind of situations in which we may need to rationalise the denominator.
When denominator is made of a single term containing a root, we simply multiply up and down (numerator and denominator) by the root itself as many times as needed, depending on the root index. This eliminates the root from denominator.
In this case, we multiply up and down by the conjugate of denominator. This allows get rid of the surd in the denominator as it raises at the second power.
When we have the root of an entire fraction involved, the first thing to do is to apply the rule
where b can also be a binomial, not just a number. Then, we use the any of the first two methods to rationalise the denominator.
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