Apply the Closure Property to predict the answer. Will the sum of 25−−√ and 18 be an irrational or rational number?(1 point)

Question

Responses

Rational, because both addends are rational.
Rational, because both addends are rational.
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.
Irrational, because one of the addends has a radical.
Irrational, because one of the addends has a radical.
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, a rational number) and 18 (also a rational number) is rational or irrational, we can use the properties of rational and irrational numbers.

1. Both \( \sqrt{25} \) and 18 are rational numbers since:

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

2. The closure property of rational numbers states that the sum of two rational numbers is always a rational number.

Therefore, the sum of \( \sqrt{25} \) and 18 is rational.

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