Question

Which of the following is an irrational number between 2 and √5? a) 2.1 b) 2.050050005... c) 2.15050505.... d) 2.0500050005

Answer 1

Answer: option b

Step-by-step explanation:

First, we have to find out the approximate value of $\sqrt5$ which is

2.236067.........
option a) is clearly rational as its decimals are ending at a point.
option c) is rational as even though its decimals are not ending but 50 is repeating in a sequence so it can be expressed as a rational number.
option d) is rational for the same reason mentioned for option c). 5000 is repeating in a sequence.

option b) is irrational as neither are the decimals ending nor are they repeating in a sequence

.: option b) is your answer.