Question
Mia says that anytime there is a radical in an addition expression, it automatically has an irrational as the sum. is she correct?
A. no, radicals always simplify to integers, so they are rational.
B. no, some radicals simplify to rational numbers.
C. yes, radicals are irrational.
D. yes, radicals cant be simplified, so they must be irrational
A. no, radicals always simplify to integers, so they are rational.
B. no, some radicals simplify to rational numbers.
C. yes, radicals are irrational.
D. yes, radicals cant be simplified, so they must be irrational
Answers
GPT-4o mini
Mia's statement is not entirely correct. The correct answer is:
**B. no, some radicals simplify to rational numbers.**
For example, \(\sqrt{4} = 2\) which is a rational number. Similarly, \(\sqrt{9} = 3\) is also rational. While many radicals do yield irrational numbers (like \(\sqrt{2}\)), not all result in irrationals, especially when the radicand is a perfect square. Therefore, the presence of a radical in an expression does not guarantee an irrational sum.
**B. no, some radicals simplify to rational numbers.**
For example, \(\sqrt{4} = 2\) which is a rational number. Similarly, \(\sqrt{9} = 3\) is also rational. While many radicals do yield irrational numbers (like \(\sqrt{2}\)), not all result in irrationals, especially when the radicand is a perfect square. Therefore, the presence of a radical in an expression does not guarantee an irrational sum.