Question

The value of \[\sqrt{3 - 2\sqrt{2}}\] is 

Options

• \[\sqrt{2} - 1\]

• \[\sqrt{2} + 1\]

• \[\sqrt{3} - \sqrt{2}\]

• \[\sqrt{3} + \sqrt{2}\]

Answer 1

Given that:`sqrt(3 -2sqrt2)` It can be written in the form   `(a-b)^2 = a^2+b^2 -2ab` as

`sqrt(3 -2sqrt2) = sqrt(2+1-2 xx 1 xxsqrt2)` 

` = sqrt((sqrt2 )^2 + (1)^2 - 2 xx 1 xx sqrt2)`

`=  sqrt((sqrt2-1)^2)`

` = sqrt2 - 1.`