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Question
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
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Solution
We are asked to simplify`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 xx sqrt2)`
` = sqrt((sqrt2)^2 + (1)^2 - 2xx 1xxsqrt2)`
` = sqrt((sqrt2 - 1)^2)`
` = sqrt2 - 1`
Hence the value of the given expression is`sqrt2 - 1`.
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