Apply the Closure Property to predict the answer. Will the sum of 25−−√

Question

and 18
be an irrational or rational number?(1 point)
Responses

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.
It could be either, because there is one of each type of number.

Rational, because both addends are rational.

Answer 1

To determine whether the sum of \( \sqrt{25} \) (which is 5) and 18 is rational or irrational, let's analyze the numbers involved:

1. Evaluate \( \sqrt{25} \): \[ \sqrt{25} = 5 \]

2. Identify the second addend: \[ 18 \text{ is a rational number.} \]

3. Add the two numbers: \[ 5 + 18 = 23 \]

4. Determine the nature of the result:

   • The result \( 23 \) is a rational number.

Now, let’s evaluate the provided response options:

1. Irrational, because one of the addends has a radical.

   • This is incorrect because \( \sqrt{25} \) simplifies to a rational number.

2. The sum does not exist because a radical cannot be added to a fraction.

   • This is incorrect; we can add a radical to a rational number if the radical is a rational value.

3. It could be either, because there is one of each type of number.

   • This is incorrect; since \( \sqrt{25} \) is rational, the sum must also be rational.

4. Rational, because both addends are rational.

   • This is the correct response.

Therefore, the correct answer is:

Rational, because both addends are rational.