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

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

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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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