Question

prove root p + root 2 irrational​

Answer 1

Answer:

Now x, x², p, q and 2 are all rational, and rational numbers are closed under subtraction and division. So (x² - p - q) / 2 is rational. But since p and q are both primes, then pq is not a perfect square and therefore √(pq) is not rational. But this is a contradiction.

Explanation:

Answer: Given √2.

To prove: √2 is an irrational number. Proof: Let us assume that √2 is a rational number. So it can be expressed in the form p/q where p, q are co-prime integers and q≠0. √2 = p/q. ...

Solving. √2 = p/q. On squaring both the side we get, =>2 = (p/q)2