Question

Which of the following are two rational numbers between $\sqrt{5}$ and $\sqrt{6}$

• A. $1\cdot 3,1\cdot 4$
• B. $2\cdot 3,2\cdot 4$
• C. $2\cdot 5,2\cdot 6$
• D. $2\cdot 6,2\cdot 7$

Answer 1

The correct option is B

$2\cdot 3,2\cdot 4$

Take two rational numbers between $\sqrt{5}$ and $\sqrt{6}$ which are perfect squares such as :

$\therefore \sqrt{5}<\sqrt{6}\Rightarrow \sqrt{5}<\sqrt{5\cdot 29}<\sqrt{5\cdot 76}<\sqrt{6}$
$\Rightarrow \sqrt{5}<2\cdot 3<2\cdot 4<\sqrt{6}$