Apply the Closure Property to predict the answer. Will the sum of sqrt(25) and irrational or rational number?

Question

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.

Answer 1

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.