Question

Insert two irrational numbers between 3 and 4.

Answer 1

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)`