In addition to the revision notes for Surds on this page, you can also access the following Powers and Roots learning resources for Surds
Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
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7.4 | Surds |
In these revision notes for Surds, we cover the following key points:
By definition, surds are all numbers representing unresolved roots of any real number. In other words, a surd is a root of a positive real quantity if its value cannot be exactly determined.
On the other hand, a transcendental number is an irrational number that is not the root of any number, meaning that it is not an algebraic number of any degree.
Hence, surds & transcendental numbers give the set of rational numbers.
Surds may belong to one (or more) of the following categories:
Surds have four main properties, where the first two are identical to the properties of roots. The properties of surds are as follows:
For any positive numbers a and b (or they may also be negative when n is odd), we have
For any positive numbers a and b (or they may also be negative when n is odd), we have
For any numbers a and b where b is positive, we have
For any numbers a, b and positive c (or it can also be negative when n is odd), we have
We can complete basic operations with surds in the same way as with all the other types of numbers.
We can add or subtract only like surds. Some surds apparently look different, but after a few operations, we can convert them into like surds.
Multiplication and division of surds is nothing more but the applications of the first two properties of surds in the reverse direction (from end to start). The only restriction is that surds must have the same index.
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