Question

Let x = √3 + √5 and y = √8 + √2. Which is greater?

• A. x=y
• B. x>y
• C. x<y
• D. cannot be determined

Answer 1

Answer:

C. x<y

Compare the two values:

$x=\sqrt{3}+\sqrt{5}$
$y=\sqrt{8}+\sqrt{2}$

Since $(\sqrt{8}=2\sqrt{2})$,

$y=2\sqrt{2}+\sqrt{2}=3\sqrt{2}$
Approximate values:

• $(\sqrt{3} \approx 1.732)$

• $(\sqrt{5} \approx 2.236)$

So,

$x \approx 1.732+2.236=3.968$

And,

$y \approx 3\times1.414=4.242$

Therefore,

y>x

So, y is greater.