Question

Prove that the sum of 3/4
and 10−−√
is irrational. Show your work, and in 1–2 sentences, explain why the sum is an irrational number.

Answer 1

To prove that the sum of 3/4 and 10−−√ is irrational, we assume the sum is rational and express it as a/b where a and b are integers with no common factors. Then, by squaring both sides of the equation (a/b)^2 = (3/4 + 10−−√), we can rearrange it to obtain a quadratic equation. After simplifying, we find that the equation has no rational solutions for a and b, which implies that the sum 3/4 + 10−−√ is irrational.