Another name for index is power (you will often say, for example, 2 to the power of three to mean 23).
In order to work with indices you need to learn the basic laws of indices listed below:
We know that √9 and √36 have exact values of 3 and 6 respectively.
However √2 and √3 does not have an exact quantity and these numbers are called irrational.
Surds are just the name given to the numbers when they are left in the form √2 and √3.
There is only one rule you need to remember:
√(ab) = √a √b
This allows us to express a number in simplest surd form:
√50 = √(2 × 25) = √2 × √25 = √2 × 5 = 5 √2
If you have a fractional answer, you must remove the surds from the denominator - this is called rationalizing the denominator.
Read the following example to see how this is done.
From our work on expanding brackets we know that (a + b)(a − b) gives a2 − b2 and we eliminate any surds contained in a or b.
So to rationalize the denominator of
we must multiply the numerator and the denominator by √6 + √5.
Multiplying the denominators gives: