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Question
Check whether the square of the following is rational or irrational:
`sqrt(2) + sqrt(3)`
Solution
`(sqrt(2) + sqrt(3))^2`
= `(sqrt(2))^2 + (sqrt(3))^2 + 2 xx sqrt(2) xx sqrt(3)`
= 2 + 3 + 2`sqrt(6)`
= 5 + 2`sqrt(6)`, which is irrational
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