Question

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

Answer 1

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^(`