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Find two irrational numbers between 2 and 2.5. - Mathematics

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Sum

Find two irrational numbers between 2 and 2.5.

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Solution

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

∴ Irrational number between 2 and 2.5 is = `sqrt(2xx2.5)=sqrt5`

Similary, irrational number between 2 and `sqrt5 `

So required numbers are `sqrt5`

Concept: Proofs of Irrationality
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