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)
A) Yes, radicals are irrational.
B) No, radicals always simplify to integers, so they are rational.
C) Yes, radicals can’t be simplified, so they must be irrational.
D) No, some radicals simplify to rational numbers.
A) Yes, radicals are irrational.
B) No, radicals always simplify to integers, so they are rational.
C) Yes, radicals can’t be simplified, so they must be irrational.
D) No, some radicals simplify to rational numbers.
Answers
GPT-4o mini
Mia is incorrect. The correct answer is:
D) No, some radicals simplify to rational numbers.
For example, \(\sqrt{4} + \sqrt{1} = 2 + 1 = 3\), which is a rational number. Therefore, having a radical in an addition expression does not automatically guarantee an irrational sum.
D) No, some radicals simplify to rational numbers.
For example, \(\sqrt{4} + \sqrt{1} = 2 + 1 = 3\), which is a rational number. Therefore, having a radical in an addition expression does not automatically guarantee an irrational sum.