Question
Mia says that anytime there is a radical in an addition expression, it automatically has an irrational number as the sum. Is she correct ? (1 point) No, radicals always simplify to integers , so they are rational Yes, radicals are irrational No, some radicals simplify to rational numbers. Yes, radicals can't be simplified , so they must be irrational
Answers
GPT-4o mini
Mia is not correct. The correct answer is: **No, some radicals simplify to rational numbers.**
For example, \(\sqrt{4} = 2\) is a rational number, despite being expressed as a radical. Additionally, if you add two radicals that both simplify to rational numbers, the sum can also be rational. For example, \(\sqrt{4} + \sqrt{1} = 2 + 1 = 3\), which is rational. So, not all expressions containing radicals will result in an irrational sum.
For example, \(\sqrt{4} = 2\) is a rational number, despite being expressed as a radical. Additionally, if you add two radicals that both simplify to rational numbers, the sum can also be rational. For example, \(\sqrt{4} + \sqrt{1} = 2 + 1 = 3\), which is rational. So, not all expressions containing radicals will result in an irrational sum.