Question

Prove that 3 + 2/5
is irrational.​

Answer 1

Correct Question:

prove that 3+√5 is irrational.

Answer:

Let us Assume that 3+√5 is rational.

Thus it can be written in the form

$\frac{a}{b} \: and \: b \: is \: not= 0$

and a and b are coprime.

Therefore

$3 + 2 \sqrt{5} = \frac{a}{b} \\ \\ 3 - \frac{a}{b} = 2 \sqrt{5} \\ \\ \frac{3b - a}{b} = \sqrt{5 }$

Since a and n are integers than we get

$\frac{3b - a}{b}$

is rational number and

√5 is also rational number.

But it is not true because √5 is irrational.

Therefore the given number 3+√5 is irrational and our assumption taken is wrong.