Question

I need 3 irrational numbers between 4 and 5

Answer 1

Using the square root is probably the easiest way to find irrationals.

Answer 2

\(\Large\rm 4^2=16\)
\(\Large\rm 5^2=25\)


Therefore \(\Large\rm \sqrt{25}=5\) and \(\Large\rm \sqrt{16}=4\).
(Because 16 and 25 are perfect squares).

But what about the square root of the values between 16 and 25?

Answer 3

The root of any value which is not a perfect square will be irrational.
\(\Large\rm \sqrt{24}\) is irrational, and since it's between \(\Large\rm \sqrt{16}\) and \(\Large\rm \sqrt{25}\) that means it's between 4 and 5.