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Question
The value of \[\sqrt{3 - 2\sqrt{2}}\] is
Options
\[\sqrt{2} - 1\]
\[\sqrt{2} + 1\]
\[\sqrt{3} - \sqrt{2}\]
\[\sqrt{3} + \sqrt{2}\]
Solution
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.`
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