Question

In the following exercises, simplify.

ⓐ $\sqrt{-49}$ⓑ$-\sqrt{256}$

Short answer

Part (a)$\sqrt{-49}$is not real number

Part (b)role="math" localid="1645018398063" $-\sqrt{256}=-16$

Step-by-step solution

Part(a) Step 1. Given information 

(a)$\sqrt{-49}$

Simplify the given value.

Step 2. Explanation

Since

Since any positive number squared is positive.

Any negative number squared is positive.

There is no real number equal to .

The square root of a negative number is not a real number.

Part (b) Sep 4. Given information

(b)$-\sqrt{256}$

Simplify the given value.

Step 4. Explanation

Since$\begin{array}{l}\Rightarrow {\left(16\right)}^2=256\\ \Rightarrow -\sqrt{256}=\sqrt{{\left(16\right)}^2}\\ \Rightarrow -16\end{array}$