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.(2 points)
1 answer
Let's assume that the sum of 3/4 and √10 is a rational number, which means it can be written as a fraction a/b where a and b are integers and b is not equal to 0. Then, 3/4 + √10 = a/b. We can rearrange this equation to get √10 = (a/b) - 3/4 = (4a - 3b)/4b. This implies that √10 is rational, but since √10 is actually irrational, our assumption is false. Therefore, the sum of 3/4 and √10 is an irrational number.