Question

√(2+√3)+√(2-√3) find the value of these numbers

Answer 1

√(2+√3)/(2-√3) => √(2+√3)/√(2-√3)

rationalizing the denominator

√(2+√3)(2+√3)/√(2-√3)(2+√3)

√(2+√3)²/√(2)²-(√3)²

2+√3/√(4-3) => 2+√3/√1. (√1 = 1)

=> 2+√3

since √3 =1.73.

2+√3 = 2+1.73 = 3.73 is the answer

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Answer 2

Let its value be x
$\sqrt{(2 + \sqrt{3}) } + \sqrt{(2 - \sqrt{3} )} = x$
squaring both sides
${{{ { \sqrt{(2 + \sqrt{3} }) + \sqrt{(2 - \sqrt{3} }) }^{2} } = {x}^{2} }}$
which gives
$2 + \sqrt{3} + 2 - \sqrt{3} + 2 \sqrt{4 - 3} = {x}^{2}$
or
$4 + 2 ( \frac{ + }{ - }1) = {x}^{2}$
putting x =1
$6 = {x}^{2}$
or
$x = \sqrt{6}$
now putting x= -1
$2 = {x}^{2}$
or
$x = \sqrt{2}$
so ans is
$x = \sqrt{6} \: or \: \sqrt{2}$
This is the right answer

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