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

1 Answer
Mar 13, 2018

#sqrt24# is real and irrational.


If you work out #sqrt24# on a calculator you will get an answer of ;

#sqrt24 = 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 and 5#.

We could get more precise and say that:

#4.898 < sqrt24 < 4.899#

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