Question
Apply the Closure Property to predict the answer. Will the sum of 25−−√ and 18 be an irrational or rational number?(1 point)
Responses
Rational, because both addends are rational.
Rational, because both addends are rational.
The sum does not exist because a radical cannot be added to a fraction.
The sum does not exist because a radical cannot be added to a fraction.
Irrational, because one of the addends has a radical.
Irrational, because one of the addends has a radical.
It could be either, because there is one of each type of number.
Responses
Rational, because both addends are rational.
Rational, because both addends are rational.
The sum does not exist because a radical cannot be added to a fraction.
The sum does not exist because a radical cannot be added to a fraction.
Irrational, because one of the addends has a radical.
Irrational, because one of the addends has a radical.
It could be either, because there is one of each type of number.
Answers
GPT-4o mini
To determine whether the sum of \( \sqrt{25} \) (which is 5, a rational number) and 18 (also a rational number) is rational or irrational, we can use the properties of rational and irrational numbers.
1. Both \( \sqrt{25} \) and 18 are rational numbers since:
- \( \sqrt{25} = 5 \) is a rational number.
- 18 is also a rational number.
2. The closure property of rational numbers states that the sum of two rational numbers is always a rational number.
Therefore, the sum of \( \sqrt{25} \) and 18 is rational.
The correct response is:
**Rational, because both addends are rational.**
1. Both \( \sqrt{25} \) and 18 are rational numbers since:
- \( \sqrt{25} = 5 \) is a rational number.
- 18 is also a rational number.
2. The closure property of rational numbers states that the sum of two rational numbers is always a rational number.
Therefore, the sum of \( \sqrt{25} \) and 18 is rational.
The correct response is:
**Rational, because both addends are rational.**