Question

Write the irrational numbers between $2$ and $7$.

Answer 1

Write irrational numbers between $2$ and $7$.

Irrational numbers are those numbers which cannot be expressed in the form of $\frac{p}{q}$, where $q\ne 0$.

The square root numbers other than perfect square numbers are irrational numbers.

It is known that,

$\begin{array}{rcl}\sqrt{4}& =& 2\\ \sqrt{49}& =& 7\end{array}$

So, the square root of number present between $4$ and $49$ are irrational numbers.

Thus, the irrational numbers between $2$ and $7$ are,

$\sqrt{5},\sqrt{6},\sqrt{7},\sqrt{8},\sqrt{10},\sqrt{11},\sqrt{12},...,\sqrt{48}$

Therefore, irrational numbers between $2$ and $7$ are $\sqrt{5},\sqrt{6},\sqrt{7},\sqrt{8},\sqrt{10},\sqrt{11},\sqrt{12},...,\sqrt{48}$.