Thread: Prove no rational number whose square is 98

Q: Prove that there is no rational number whose square is 98

Here is what i have so far:

Suppose, for contradiction, that there is a rational number a/b with gcd(a,b)=1 whose square is 98.

(a/b)^2=98
a^2=98b^2
a^2=2(49)b^2

So, does this show that a is even? how do i show that b is even to get a contradiction?

You are on the right way:

Suppose, for contradiction, that there is a rational number a/b with gcd(a,b)=1 whose square is 98.

(a/b)^2=98
a^2=98b^2
(a^2 / (49 b^2) = 2
(a/7b) = sqrt(2) (or (a/7b) = - sqrt(2))
(a/c) = sqrt(2)
=> sqrt(2) is a rational number
=> Contradiction.