prove that 3+root 2 is irrational

#Maths #Rational Numbers #Numbers

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prove that 3+root 2 is irrational

Afrid khan 25th Feb, 2026

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Answer (1)

Divya Sharma 11th Mar, 2026

Let's assume that 3+ √2 is rational,

Then,

√2 = (3+√2) - 3

The difference of two rational numbers is rational. So this would imply √2 is rational.

But √2 is irrational, therefore, 3+√2 is irrational

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