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.

Rational, because both addends are rational.
Rational, because both addends are rational.

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

Answer 1

To determine whether the sum of \( \sqrt{25} \) (which is 5 and definitely a rational number) and 18 (also a rational number) is rational or irrational, we can apply the properties of rational and irrational numbers.

1. Identify the types of numbers:

   • \( \sqrt{25} = 5 \) is a rational number.
   • 18 is also a rational number.

2. Closure property of rational numbers: The sum of two rational numbers is always a rational number.

Given that both \( 5 \) (from \( \sqrt{25} \)) and \( 18 \) are rational, their sum \( 5 + 18 = 23 \) is also rational.

Thus, the correct response is: Rational, because both addends are rational.