Question

prove that √3+2√5 is irrational​

Answer 1

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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

Answer 2

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