Question

Find $3$ irrational numbers between $\sqrt{2}$ and $\sqrt{3}$ .

Answer 1

Step 1: Define irrational numbers and convert the given irrational numbers into decimals

Irrational Number:

1. A number that is not a rational number is said to be an irrational number.
2. Every non-terminating decimal is an irrational number.

The given two irrational numbers are $\sqrt{2}$ and $\sqrt{3}$ .

We know, $\sqrt{2}=1.4142135623...$

And, $\sqrt{3}=1.7320508075...$

Step 2: Select any three non-terminating decimals between the above two

Any three non-terminating decimals can be selected randomly between $1.4142135623...$ and $1.7320508075...$

So, three nonterminating decimals between the above two are $1.52585...,1.62482...$ and $1.71371...$

Hence, the three irrational numbers between $\sqrt{\mathbf{2}}$ and $\sqrt{\mathbf{3}}$ are $\mathbf{1}\mathbf{.}\mathbf{52585}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{,}\mathbf{}\mathbf{1}\mathbf{.}\mathbf{62482}\mathbf{.}\mathbf{.}\mathbf{.}$ and $\mathbf{1}\mathbf{.}\mathbf{71371}\mathbf{.}\mathbf{.}\mathbf{.}$.