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.
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 \( \sqrt{25} \) (which simplifies to 5) and 18 is rational or irrational, we first simplify the expression:

\[ \sqrt{25} + 18 = 5 + 18 = 23. \]

Since both \( \sqrt{25} \) (which is a rational number) and 18 (which is also a rational number) are being summed, the result (23) is also a rational number.

The correct response is:

Rational, because both addends are rational.