Log in to add a comment

Log in to add a comment

x^2 = (√7)^2

x^2 = 7

(a/b)^2 = 7

a^2 = 7b^2

So a must be a multiple of 7. Let a = 7k for some integer k. Then:

(7k)^2 = 7b^2

49k^2 = 7b^2

7k^2 = b^2

Now, b must also be a multiple of 7. But this contradicts the fact that a/b is in simplest form. So our assumptions that √7 is rational must be false.