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प्रश्न
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
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उत्तर
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+2xx 1xx sqrt2)`
` = sqrt((sqrt2)^2 + (1)^2 + 2 xx 1 xx sqrt2)`
` = sqrt((sqrt2+1))^2`
` = sqrt2 +1`
Hence the value of given expression is ` sqrt2 +1`.
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