Find three irrational numbers between 2 and 2.5 .

Question

Philoid · Accepted Answer

If a and b are any two distinct positive rational numbers such that ab is not a perfect square, then the irrational number

lies between a and b.
∴ Irrational number between 2 and 2.5 is

, i.e

Irrational number between 2 and

is

= 2^(1/2) × 5^(1/4)
Irrational number between

and 2.5 is

=
Thus, the three irrational numbers between 2 and 2.5 are

, 2^(1/2) × 5^(1/4)and (1/2) × 5× 2.