Question

current objective
simplify expressions with square roots

question

simplify: \\(\sqrt{-49}\\). if the result is not a real number, enter \\(\varnothing\\).

provide your answer below:

Explanation:

Identify the radicand and its domain

$$ \sqrt{-49} $$

The radicand is \(-49\), which is less than \(0\).

Determine if the square root is a real number

For any real number \(x\), if \(x < 0\), then \(\sqrt{x}\) is not a real number.

$$ -49 < 0 \implies \sqrt{-49} otin \mathbb{R} $$

Apply the given instruction for non-real results

The problem states: "If the result is not a real number, enter \(\varnothing\)."

$$ \text{Result} = \varnothing $$

Answer:

Simplify: \(\sqrt{-49}\). If the result is not a real number, enter <blank>\(\varnothing\)</blank>.