Question

Show that 3+root2 is irrational

Answer 1

Let 3+root 2 be rational...
Ok?
Then...
If we subtract 3 which is a rational no....
(3+root 2)- 3
We get..
Root 2 which is also rational because
(rational - rational) = rational
But we know that root 2 is Irrational so
This contradicts the fact that root 2 is Irrational
Since this contradiction arises from 3+ root2 is
Rational so
Therefore it is Irrational...

Answer 2

Hi Friend !!!

Here is ur answer !!

Let's assume that 3+√2 is a rational number


3+√2 = p/q

3 = p/q - √2

3² = (p/q - √2)²

9 = p²/q²- 2(p/q) (√2)+ 4

9-4 = p²/q²-2√2p/q

2√2p/q = p²/q² - 5

√2 = (p²-5q²/q²)(q/2p)

√2 = p²-5q²/2pq

If p, q are integers then p²-5q²/2pq is rational number


Then √2 also rational number

But it contradicts the fact that √2 is irrational

So, our assumption is wrong

So, 3+√2 is irrational

HENCE PROVED


Hope it helps u : )