1.4 Roots and fractional indices

To see what fractional indices mean in practice a good place to start is with this example:

Using Rule 3 and 1 this can be written as follows:

This shows that 2^1/2 is a way to represent the square root of 2. Since .

Extending this a^1/3 is the cube root of a and can be written as . a^1/4 is the fourth root of a, written as .

So it follows that:

a^1/n is the nth root of a and can be written as .

If you use Rule 3 to write a^p/q as , you should now be able to see that a^p/q is the qth root of a^p which is written as .

So,

Rules 1, 2, and 3 all work with fractional indices.

Before moving on to another topic, you’ll learn what the power of zero means.