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Question
Insert five irrational number's between `2sqrt(3) and 3sqrt(5)`.
Solution
We know that `2sqrt(3) = sqrt(4 xx 3) = sqrt(12) and 3sqrt(5) = sqrt(9 xx 5) = sqrt(45)`.
Thus, we have `sqrt(12) < sqrt(13) < sqrt(14) < sqrt(17) < ...... < sqrt(43) < sqrt(44) < sqrt(45)`
So, any five irrational numbers between `2sqrt(3) and 3sqrt(5)` are :
`sqrt(13), sqrt(14), sqrt(23), sqrt(37), sqrt(41)`
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