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Find two irrational numbers lying between √2 and √3 - CBSE Class 10 - Mathematics

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Question

Find two irrational numbers lying between `sqrt2" and "sqrt3`

Solution

We know that, if a and b are two distinct positive irrational numbers, then `sqrt(ab)` is an irrational number lying between a and b.

∴ Irrational number between `sqrt2 ` is = `sqrt(sqrt2xxsqrt3) = 6^(`

Irrational number between `sqrt2 `is `sqrt(sqrt2xx6^(1/4)) = 2^(`

Hence required irational number are `6^(`

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Solution Find two irrational numbers lying between √2 and √3 Concept: Proofs of Irrationality.
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