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Revision:Indices and SurdsTSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Indices and Surds Indices are used to describe the general term for
Laws of Indices
Examples
SurdsSurds are basically an expression involving a root, squared or cubed etc... There are some basic rules when dealing with surds
Also notice the special case
Difference of Two Squares
Rationalising SurdsWhen you have a fraction where both the nominator and denominator are surds, rationalising the surd is the process of getting rid of the surd on the denominator. To rationalise a surd you multiply top and bottom by fraction that equals one. Take the example shown below
To rationalise this multiply by effectively 1
Can you see why For a more complex term
First of all, we need to get rid of the surd expression on the bottom, you should remember the difference of two squares formula.
suppose a = 1 and b =
So to get rid of the denominator surd we multiply
In general
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![a^{\frac{1}{m}} = \sqrt[m]{a}](http://www.thestudentroom.co.uk/latexrender/pictures/cf/cfff19b1e977386adf87edba893f0c58.png "a^{\frac{1}{m}} = \sqrt[m]{a}")
![a^{\frac{m}{n}} = \sqrt[n]a^m](http://www.thestudentroom.co.uk/latexrender/pictures/92/92d1629f9a2b1e0c7bc2a232d02fb41f.png "a^{\frac{m}{n}} = \sqrt[n]a^m")
![\sqrt[5]4^3 = (4^3)^{\frac{1}{5}} = (4^{\frac{3}{5}})](http://www.thestudentroom.co.uk/latexrender/pictures/86/86797b891d7d8e22dd885327fc883dbf.png "\sqrt[5]4^3 = (4^3)^{\frac{1}{5}} = (4^{\frac{3}{5}})")
