Question

An irrational number between 5 and 6 is

(a)$\frac{1}{2}(5+6)$ (b)$\sqrt{5+6}$ (c)$\sqrt{5\times 6}$ (d) none of these

Answer 1

$\frac{1}{2}(5+6)=\frac{1}{2}\left(11\right)=\frac{11}{2},rational$

$\sqrt{5+6}=\sqrt{11}=3.317$

$\sqrt{5\times 6}=\sqrt{30}=5.477$

An irrational number between 5 and 6 is (c) $\sqrt{5\times 6}$