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

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

Solution

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

Concept: Concept of Irrational Numbers
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