Maths for Diploma Studies

So far, we have used the term ‘base number’ to describe the number subject to the exponent. It can be described as another term, and that is the root.

We use square and cube roots, referring to numbers that have been squared or cubed by the exponents 2 and 3, respectively. For higher exponents, we use n^th root, for example, 4^th_, 5^th, and 6^th roots.

Figure: Relationship between exponents and roots

For example:

In the above, the root is squared to get the result, so if we take a square root of the result, we get back to the root:

To show a cube root, we use a 3 above the root symbol or radical sign like so:

Which, as we now know, is the opposite of:

As any number squared must be a positive number (remember from earlier that if we multiply a negative number by a negative number, we produce a positive answer), we cannot calculate the square root of a negative number. We can, however, calculate cube and n^th roots for negative values. For example:

To help reinforce what we have just learned, on the next page there are some practice questions. Answers and explanations can be revealed by clicking on show answer.