Question

An irrational number between 2 and 2.5 is

A. \(\sqrt{11}\)

B. \(\sqrt5\)

C. \(\sqrt{22.5}\)

D. \(\sqrt{12.5}\)

Answer 1

Note: If a and b are two positive numbers, such that the product of a and b is not a perfect square of a rational number, then, \(\sqrt{ab}\) is an irrational number lying between "a" and "b".

So, now we have two numbers 2 and 2.5.

Now the product of these two number is 5, which is not a perfect square. So, we can say that √5 is an irrational number lying between "2" and "2.5" 

√5= 2.23606797749978969, Which is a non– terminating and non- repeating decimal. Thus, option B is the correct answer.