Question

prove 3+ 4underroot 2 is irrational

Answer 1

3 + 4√2 is irrational number

__________ [TO PROVE]

Let us assume that, 3 + 4√2 is a rational number

=> 3 + 4√2 = $\dfrac{a}{b}$

Here, a and b are co-prime numbers.

=> 4√2 = $\dfrac{a}{b}$ - 3

=> 4√2 = $\dfrac{a\:-\:3b}{b}$

=> √2 = $\dfrac{a\:-\:3b}{4b}$

Here..

$\dfrac{a\:-\:3b}{4b}$ is rational number.

So, √2 is also a rational number.

But we know that √2 is irrational number.

So, our assumption is wrong.

3 + 4√2 is irrational number.

___________ [HENCE PROVED]