# Prove that of the Numbers  2 - Sqrt(3) is Irrational: - Mathematics

Prove that of the numbers   2 - sqrt(3)  is irrational:

#### Solution

Let 2 - sqrt (3) be rational.
Hence, 2 and 2 - sqrt (3) are rational.

∴ (2 - 2 + sqrt (3)  ) = sqrt (3) = rational [∵ Difference of two rational is rational]
This contradicts the fact that  sqrt (3)  is irrational.
The contradiction arises by assuming 2 -  sqrt (3)  is rational.
Hence, 2 - sqrt (3) is irrational.

Concept: Concept of Irrational Numbers
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