Question

Suppose x = √2 + √3, y = √5 + √1, and z = 2√2 + 1. ; then which of the following is true?

• A. x <y < z
• B. z < y < x
• C. y < x < z
• D. x < z < y

Answer 1

Answer:

A. x <y < z

Approximate the values:

$x = \sqrt{2} + \sqrt{3} \approx 1.414 + 1.732 = 3.146$
$y = \sqrt{5} + \sqrt{1} = 2.236 + 1 = 3.236$
$z = 2\sqrt{2} + 1 \approx 2(1.414) + 1 = 3.828$

Therefore,

\boxed{z > y > x}