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Question
Insert two irrational numbers between 3 and 4.
Solution
Since 3 and 4 are rational numbers and 3 x 4 = 12 is not a perfect square.
∴ One irrational number between 3 and 4 = `sqrt(3 xx 4) = sqrt(12)`
And , an irrational number between 3 and `sqrt(12) = sqrt(3 xx sqrt(12)) = sqrt(3sqrt(12)`
∴ Required irrational numbers between 3 and 4 are : `sqrt(12) and sqrt(3sqrt(12)`
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