Q37 / 59 · KVPY 2013 (SA) · Mathematics

The least positive integer $n$ for which $\sqrt{n+1}-\sqrt{n-1} < 0.2$ is

A
$24$
B
$25$
Correct answer
C
$26$
D
$27$

Solution

$\sqrt{n+1} < 0.2+\sqrt{n-1}$ squaring $1.96 < .4 \sqrt{n-1}$ again squaring $(4.9)^{2}+1 < n$

Hence, the correct answer is option: 'C'.

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