Question

Prove that 3+√5 is an irrational nuber​

Answer 1

Answer

3 + √5 = a/b

[Here a and b are co-prime numbers, where b ≠ 0

√5 = a/b - 3

√5 = (a - 3b)/b

Here, {(a - 3b)/b} is a rational number.

But we know that √5 is an irrational number.

So, {(a - 3b)/b} should also be an irrational number.

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Answer 2

Hence 3+√5 is an irrational number