# Prove that of the Numbers 5 + 3 Sqrt (2) is Irrational: - Mathematics

Prove that of the numbers 5 + 3 sqrt (2)  is irrational:

#### Solution

Let,5 + 3 sqrt (2) be rational.
Hence, 5 and 5 + 3 sqrt (2) are rational.
∴ (5 + 3 sqrt (2) – 5) = 3sqrt(2) = rational       [∵Difference of two rational is rational]
∴ 1/3 × 3sqrt(2) = sqrt(2) = rational     [∵Product of two rational is rational]
This contradicts the fact that sqrt(2) is irrational.
The contradiction arises by assuming 5 + 3 sqrt (2) is rational.
Hence, 5 + 3 sqrt (2) is irrational.

Concept: Concept of Irrational Numbers
Is there an error in this question or solution?