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

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

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

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 \( 18 \) is rational or irrational, let's first simplify the expression.

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

2. Now add \( 5 \) (which is rational) and \( 18 \) (also rational): \[ 5 + 18 = 23 \]

Since both \( 5 \) and \( 18 \) are rational numbers, their sum \( 23 \) is also a rational number.

Based on this analysis, the correct response is:

Rational, because both addends are rational.