# What is the set of numbers to which sqrt24 belongs?

Mar 13, 2018

$\sqrt{24}$ is real and irrational.

#### Explanation:

If you work out $\sqrt{24}$ on a calculator you will get an answer of ;

$\sqrt{24} = 4.898979486$

But the number does not stop there. it continues after the last $6$, but you will notice that there is no pattern emerging.

This type of number is called an irrational number because it cannot be written as a fraction which would represent an exact ratio between two integers,

It is clear that the number is on the number line somewhere - It is therefore a real number. It is between $4 \mathmr{and} 5$.

We could get more precise and say that:

$4.898 < \sqrt{24} < 4.899$

So although the exact value is not known, we can guess where it lies with some accuracy.