Question

tell if the square root is rational, irrational, or not a real number. if the square root is a real number, find the value, rounding to two decimal places.

\\\sqrt{-121}\\

is the square root rational, irrational, or not a real number?

• irrational
• rational
• not a real number

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

a. \\(\sqrt{-121} = \\)
(type an integer or a decimal. round to the nearest hundredth as needed.)

b. the square root is not a real number.

Explanation:

⚡ Using what you learned: Real Number System Overview

Step 1: Analyze the radicand

The given expression is:

$$ \sqrt{-121} $$

The value inside the square root (the radicand) is \( -121 \), which is a negative number.

Step 2: Apply real number rules

In the real number system, the square root of a negative number is not defined because no real number multiplied by itself results in a negative value:

$$ x^2 \ge 0 \quad \text{for any real number } x $$

Therefore, \( \sqrt{-121} \) is not a real number.

Answer:

• Is the square root rational, irrational, or not a real number?
• Not a real number

• Select the correct choice below and fill in any answer boxes in your choice.
• B. The square root is not a real number.