# Prove that of the Numbers Sqrt (6)  is Irrational: - Mathematics

Prove that of the numbers sqrt (6)  is irrational:

#### Solution

Let sqrt(6)  = sqrt(2) × sqrt(3) be rational.
Hence, sqrt(2) ,  sqrt(3) are both rational.
This contradicts the fact that  sqrt( 2) ,   sqrt(3 )  are irrational.
The contradiction arises by assuming sqrt(6) is rational.
Hence, sqrt(6) is irrational.

Concept: Concept of Irrational Numbers
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