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.
Irrational, because one of the addends has a radical.
Irrational, because one of the addends has a radical.
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.
It could be either, because there is one of each type of number.
and 18
be an irrational or rational number?(1 point)
Responses
Rational, because both addends are rational.
Rational, because both addends are rational.
Irrational, because one of the addends has a radical.
Irrational, because one of the addends has a radical.
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.
It could be either, because there is one of each type of number.
Answers
GPT-4o mini
To determine whether the sum of \( \sqrt{25} \) and \( 18 \) is rational or irrational, let’s analyze the components.
1. **Identifying the components**:
- \( \sqrt{25} = 5 \), which is a rational number.
- \( 18 \) is also a rational number.
2. **Applying Closure Property**: The closure property for addition states that the sum of two rational numbers is rational. Since both 5 and 18 are rational numbers, their sum must also be rational.
Therefore, the correct response is:
**Rational, because both addends are rational.**
1. **Identifying the components**:
- \( \sqrt{25} = 5 \), which is a rational number.
- \( 18 \) is also a rational number.
2. **Applying Closure Property**: The closure property for addition states that the sum of two rational numbers is rational. Since both 5 and 18 are rational numbers, their sum must also be rational.
Therefore, the correct response is:
**Rational, because both addends are rational.**