Question

prove that 3+√2 is irrational​

Answer 1

Answer:

Step-by-step explanation:

Ok, so the proof goes like this:

We prove it by contradiction: any rational number can be written as the ratio of two integers p and q, which are coprime (this is the definition of a rational number)

So, suppose 2–√3 is rational:

2–√3=pq

but then

2=p3q3

p3=2q3

This therefore means that p3 is an even number (2n is an even number for all integer n) . From the properties of multiplication, we can then deduce that if p3 is even, p is even.

So we can rewrite p=2n, for some unknown, integer n.

Therefore (2n)3=2q3

8n3=2q3

q3=4n3

Now we repeat the even argument - show that q is also even (all multiples of 4 are even), and since p and q are both even, they are not coprime,...