Question

determine whether \\(\sqrt{28}\\) is rational, irrational, or not a real number.

is \\(\sqrt{28}\\) rational, irrational, or not a real number?

rational

irrational

not a real number

select the correct choice below and fill in any answer boxes in your choice.

a. \\(\sqrt{28} = \\)
(type an integer or decimal rounded to two decimal places as needed.)

b. the square root is not a real number.

Explanation:

⚡ Using what you learned: Real Number System Overview

Step 1: Classify the number

The number inside the radical is \( 28 \). Since \( 28 \) is positive, its square root is a real number.

Because \( 28 \) is not a perfect square (the closest perfect squares are \( 25 = 5^2 \) and \( 36 = 6^2 \)), its square root cannot be written as a terminating decimal or a simple fraction. Therefore, \( \sqrt{28} \) is an irrational number.

Step 2: Approximate the value

Calculate the square root of \( 28 \):

$$ \sqrt{28} \approx 5.291502622... $$

Rounding to two decimal places:

$$ \sqrt{28} \approx 5.29 $$

Answer:

• Is \( \sqrt{28} \) rational, irrational, or not a real number?

irrational

• Select the correct choice below and fill in any answer boxes in your choice.

A. \( \sqrt{28} = 5.29 \)