Question

Which of the following are five irrational numbers between $2\sqrt{5}$

and $3\sqrt{3}$

• A. $\sqrt{2},\sqrt{3},\sqrt{5},\sqrt{7},\sqrt{8}$
• B. $\sqrt{6},\sqrt{7},\sqrt{8},\sqrt{9},\sqrt{10}$
• C. $\sqrt{30},\sqrt{31},\sqrt{32},\sqrt{33},\sqrt{34},\sqrt{35}$
• D. $\sqrt{21},\sqrt{22},\sqrt{23},\sqrt{24},\sqrt{25},\sqrt{26}$

Answer 1

The correct option is D

$\sqrt{21},\sqrt{22},\sqrt{23},\sqrt{24},\sqrt{25},\sqrt{26}$

$2\sqrt{5}=\sqrt{2^2\times 5}$

= $\sqrt{20}$

3 $\sqrt{3}=\sqrt{3^2\times 3}$

= $\sqrt{27}$

Hence five irrational numbers between

$\sqrt{20}$ and $\sqrt{27}$ are $\sqrt{21},\sqrt{22},\sqrt{23},\sqrt{24},\sqrt{25},\sqrt{26}$

Hence (D)