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)
Responses
No, radicals always simplify to integers, so they are rational.
No, radicals always simplify to integers, so they are rational.
No, some radicals simplify to rational numbers.
No, some radicals simplify to rational numbers.
Yes, radicals are irrational.
Yes, radicals are irrational.
Yes, radicals can’t be simplified, so they must be irrational.
Yes, radicals can’t be simplified, so they must be irrational.
Responses
No, radicals always simplify to integers, so they are rational.
No, radicals always simplify to integers, so they are rational.
No, some radicals simplify to rational numbers.
No, some radicals simplify to rational numbers.
Yes, radicals are irrational.
Yes, radicals are irrational.
Yes, radicals can’t be simplified, so they must be irrational.
Yes, radicals can’t be simplified, so they must be irrational.
Answers
GPT-4o mini
Mia is not correct. The correct response is:
**No, some radicals simplify to rational numbers.**
For example, \(\sqrt{4} = 2\) is a radical that simplifies to a rational number. Thus, not all radicals are irrational, and their presence in an addition expression does not guarantee that the sum will be irrational.
**No, some radicals simplify to rational numbers.**
For example, \(\sqrt{4} = 2\) is a radical that simplifies to a rational number. Thus, not all radicals are irrational, and their presence in an addition expression does not guarantee that the sum will be irrational.