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Question:

Prove that 3 + 2โ5 is irrational.

Answer:

**Proof: To prove that 3 + 2√5** **is an irrational number **

**Let us assume that 3 + 2**√**5** ** is rational. Then 3 + 2√5** ** = **

**Since a and b are co primes with only 1 common factor and b≠0. **

**⇒ 3 + 2√5** ** = **

**⇒ 2√5** ** = ** ** – 3**

**Now divide by 2 into both sides, we get**

**⇒** **√5** ** = **

**Here a and b are integer so ** **is a rational number, so** **√5** **โ should be a rational number.**

**But √5 is an irrational number, so it is contradicted.
Therefore, 3 + 2√5**

**is an irrational number.**

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