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
Yes, radicals can’t be simplified, so they must be irrational.
Yes, radicals can’t be simplified, so they must be irrational.
Yes, radicals are irrational.
Yes, radicals are irrational.
No, some radicals simplify to rational numbers.
No, some radicals simplify to rational numbers.
No, radicals always simplify to integers, so they are rational.
Responses
Yes, radicals can’t be simplified, so they must be irrational.
Yes, radicals can’t be simplified, so they must be irrational.
Yes, radicals are irrational.
Yes, radicals are irrational.
No, some radicals simplify to rational numbers.
No, some radicals simplify to rational numbers.
No, radicals always simplify to integers, so they are rational.
Answers
GPT-4o mini
Mia's statement is not correct. The correct response is:
**No, some radicals simplify to rational numbers.**
For example, \(\sqrt{4} = 2\), which is a rational number. There are also other cases where the sum of a radical and a rational number can still result in a rational number, depending on the specific values involved. Therefore, having a radical in an addition expression does not automatically mean that the result will be irrational.
**No, some radicals simplify to rational numbers.**
For example, \(\sqrt{4} = 2\), which is a rational number. There are also other cases where the sum of a radical and a rational number can still result in a rational number, depending on the specific values involved. Therefore, having a radical in an addition expression does not automatically mean that the result will be irrational.