Simplest Form of a Surd A surd is said to be in its simplest form if the number under the root sign has no perfect square as a factor. To simplify a surd, write the number under the root sign as the product of two factors, one of which is the largest perfect square. Recall that the numbers 1, 4, 9, 16, 25, 36, 49, Example 4. The square numbers are 1, 4, 9, 16, 25, 36, 49, By trying each one in turn, we find that the largest perfect square that is a factor of 72 is Example 6.
All rights reserved. Australian Business Number 53 If you experience difficulties when using this Website, tell us through the feedback form or by phoning the contact telephone number. Rules of working with surds are outlined and it is demonstrated how they can be simplified and rationalised. Adding and subtracting surds are simple- however we need the numbers being square rooted or cube rooted etc to be the same. However, if the number in the square root sign isn't prime, we might be able to split it up in order to simplify an expression.
It is untidy to have a fraction which has a surd denominator. This can be 'tidied up' by multiplying the top and bottom of the fraction by a particular expression.
This is known as rationalising the denominator, since surds are irrational numbers and so you are changing the denominator from an irrational to a rational number. Now multiply the top and bottom of the fraction by this. You can find out more about surds by clicking here. Skip to main content.
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