Question

Prove5+√2 is irrational

Answer 1

Answer:

Let assume that 5+ √ 2 is rational number.

We can write it in p/q form

Where p and q are co primes. and q ≠ 0

$5 + \sqrt{2} = \frac{p}{q}$

$\sqrt{2} = \frac{p}{q} - 5$

$\sqrt{2} = \frac{p - 5q}{q}$

So , p , 5q and q are integers so they are rational number. But it contradict the fact that√2 is irrational number.

So our hypothesis is wrong.

5+√2 is an irrational number

Hence proved