Question
Apply the Closure Property to predict the answer. Will the sum of sqrt(25) and irrational or rational number?
1/5 be an Irrational, because one of the addends has a radical. It could be either, because there is one of each type of number. Rational, because both addends are rational. The sum does not exist because a radical cannot be added to a fraction.
1/5 be an Irrational, because one of the addends has a radical. It could be either, because there is one of each type of number. Rational, because both addends are rational. The sum does not exist because a radical cannot be added to a fraction.
Answers
GPT-4o mini
To determine whether the sum of \(\sqrt{25}\) and \(\frac{1}{5}\) is rational or irrational, let's analyze each component.
1. **Evaluate \(\sqrt{25}\)**:
\[
\sqrt{25} = 5
\]
which is a rational number.
2. **Identify \(\frac{1}{5}\)**:
\(\frac{1}{5}\) is also a rational number.
3. **Sum the two rational numbers**:
\[
5 + \frac{1}{5}
\]
To add these, convert \(5\) to a fraction:
\[
5 = \frac{25}{5}
\]
Now, add the two fractions:
\[
\frac{25}{5} + \frac{1}{5} = \frac{25 + 1}{5} = \frac{26}{5}
\]
Since \(\frac{26}{5}\) is a rational number, we conclude that the sum of \(\sqrt{25}\) (which is 5) and \(\frac{1}{5}\) is rational.
Therefore, the correct answer is: **Rational, because both addends are rational.**
1. **Evaluate \(\sqrt{25}\)**:
\[
\sqrt{25} = 5
\]
which is a rational number.
2. **Identify \(\frac{1}{5}\)**:
\(\frac{1}{5}\) is also a rational number.
3. **Sum the two rational numbers**:
\[
5 + \frac{1}{5}
\]
To add these, convert \(5\) to a fraction:
\[
5 = \frac{25}{5}
\]
Now, add the two fractions:
\[
\frac{25}{5} + \frac{1}{5} = \frac{25 + 1}{5} = \frac{26}{5}
\]
Since \(\frac{26}{5}\) is a rational number, we conclude that the sum of \(\sqrt{25}\) (which is 5) and \(\frac{1}{5}\) is rational.
Therefore, the correct answer is: **Rational, because both addends are rational.**