Question

$\huge \tt \color{navy}question\\ \fbox \color{red}prove that 3+2√5 is irrational.$
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Answer 1

Given :-

3 + 2√5

To prove: 3 + 2√5 is an irrational number.

Proof :-

Let us assume that 3 + 2√5 is a rational number.

So, it can be written in the form a/b

3 + 2√5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving 3 + 2√5 = a/b we get,

»» 2√5 = a/b – 3

»» 2√5 = (a-3b)/b

»» √5 = (a-3b)/2b

This shows (a-3b)/2b is a rational number. But we know that √5 is an irrational number.

So, it contradicts our assumption. Our assumption of 3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number

______________________

Hence proved

Answer 2

Answer:

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