Question

Which of the following is greater:

$A=\sqrt{8}+\sqrt{7}$ and $B=\sqrt{10}+\sqrt{5}.$

• A. A
• B. B
• C. Both are equal
• D. Data insufficient

Answer 1

The correct option is A A

Since there is a positive sign, squaring both the surds we get
$A^2={(\sqrt{8}+\sqrt{7})}^2=8+7+2\sqrt{56}=15+2\sqrt{56}$
$B^2={(\sqrt{10}+\sqrt{5})}^2=10+5+2\sqrt{50}=15+2\sqrt{50}$
As $=56>50,15+2\sqrt{56}>15+2\sqrt{50}$
$\Rightarrow A>B$ i.e., $\sqrt{8}+\sqrt{7}>\sqrt{10}+\sqrt{5}$