Prove 3+V5 is irrational

1.	Prove 3+V5 is irrational
Answer» Let us assume that 3 + √5 is a rational number. Now, 3 + √5 = (p /q) [Here p and q are co-prime numbers] √5 = [(p /q) - 3] √5 = [(p - 3q) / q] Here, {(p - 3q) /q} is a rational number. But we know that √5 is a irrational number. So, {(p - 3q) /q} is also a irrational number. So, our assumption is wrong. 3 + √5 is a irrational number. Hence, proved. Like if you find it useful

Answer»

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

Now,

3 + √5 = (p /q)

[Here p and q are co-prime numbers]

√5 = [(p /q) - 3]

√5 = [(p - 3q) / q]

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

But we know that √5 is a irrational number.

So, {(p - 3q) /q} is also a irrational number.

So, our assumption is wrong.

3 + √5 is a irrational number.

Hence, proved.

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