Which of these is an IRRATIONAL number lying between 2 and 3?

Class 9Number SystemsNumber Systems

Step-by-Step Solution

Between 2 and 3 means between

4

and

9

, so any

n

with

4 < n < 9

works:

5

≈ 2.236.

3

≈ 1.73 is too small,

10

≈ 3.16 is too big, and

\frac{5}{2}

is in range but rational.

Answer: D)

5

**Sum/difference of two irrationals can be rational.** Example:

(1 + 2) + (1 - 2) = 2

.
**Product of two irrationals can be rational.** Example:

2 \times 2 = 2

.
**Sum of a rational and an irrational is always irrational.**

3 + 2

is irrational.
**Product of a non-zero rational and an irrational is always irrational.**

5 \times 2

is irrational.

These facts let you build new irrationals and prove things irrational by contradiction.

Don't just memorise the answer — build a daily practice habit.