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

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.

Answer 1

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.