Question

prove thate 3+√2 is irrational​

Answer 1

Answer:

The given term is irrational

Step-by-step explanation:

Answer 2

Question :–

prove thate 3+√2 is irrational.

Prove :–

Let,

3 + √2 = $\sf \dfrac{a}{b}$ is a rational number.

Where a & b are integers and b ≠ a.

$\tt \dfrac{3- a}{b} = \sqrt{2}$

$\tt\dfrac{3b - a}{b} = \sqrt{2}$

Since, a & b are integers.

So, (3b - a) and b are also integers. Therefore, $\tt\dfrac{3b - a}{b}$ is a rational number.

But we know that, √2 is a Irrational (IR).

Its L.H.S. = Rational

and R.H.S. = Irrational number.

It is not possible.

Hence, 3 + √2 is an IR (Irrational)