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Insert a rational and an irrational number between 2 and 3. - Mathematics

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Sum

 Insert a rational and an irrational number between 2 and 3.

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Solution

If a and b are two positive rational numbers such that ab is not a perfect square of a rational number, then `sqrt(ab)` is an irrational number lying between a and b.

Also, if a,b are rational numbers, then `(a+b)/2` is a rational number between them.
∴ A rational number between 2 and 3 is `(2+3)/2` = 2.5

An irrational number between 2 and 3 is = `sqrt(2xx3)=sqrt6`

Concept: Proofs of Irrationality
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