Apply the Closure Property to predict the answer. Will the sum of 25−−√ and 1/8 be an irrational or rational number?(1 point)

Question

Responses

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.

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 analyze the sum of \( \sqrt{25} \) and \( \frac{1}{8} \), we first simplify \( \sqrt{25} \):

\[ \sqrt{25} = 5 \]

Now we need to evaluate the sum:

\[ 5 + \frac{1}{8} \]

To add these two numbers, we can convert \( 5 \) into a fraction with a common denominator:

\[ 5 = \frac{40}{8} \]

Now we can add them:

\[ \frac{40}{8} + \frac{1}{8} = \frac{41}{8} \]

Since \( \frac{41}{8} \) is a fraction, it is a rational number.

So the correct answer is:

Rational, because both addends are rational.