Surds · 3 min read

Introduction to Surds

In Mathematics, we always try to write our final answers in a way that is neat and correct so that we do not lose any part of the value.

Surds are the square roots of numbers that do not have a whole number as their result, so they remain under the root sign to keep their exact value.

A surd is an irrational root of a rational number.

This means that when you try to find the root of a number and it gives you a decimal that never ends, we just leave it inside the root sign.

For example, let us look at the square root of 5. If you use a calculator, you will see that root 5 is equal to 2.236067977499789 and the numbers just keep going on and on. You can see that we have to leave out some numbers because the value never ends.

To stop this problem without being told to write the answer to two decimal places, we choose to leave our answer in surd form.

This means we can just write the answer as root 5. This way, we do not have to worry about the long decimal part that never stops.

Key points

•Final answers in Mathematics should be presented in a neat and complete context.
•Numbers like √(5) have unending decimal expansions (e.g., 2.236067977...).
•To avoid losing precision or truncating unending decimals, answers can be left in surd form.
•Leaving an answer in surd form (e.g., √(5)) ensures full accuracy without decimal approximations.