Explore

Negative Square Roots Solutions

• The rules to simplify radical expressions are only true when the radicands are    real numbers ℝ    .
• However, because the number i is the principal square root of –1, or $i=\sqrt{–1}$, problems that have a    negative     radicand can now be simplified using the    imaginary unit    .
• Therefore,    –1     must be simplified out of the radicand first. Then the remaining radicand can be simplified, if possible. 

Note

In Algebra 1, you wrote “no real solution” for a result that included a square root with a negative radicand. While that is still true, now you can simplify the radicand using imaginary numbers. This will be discussed further in the next video.

Example 3

Simplify.

$\sqrt{–16}$

Note

You can write –1 in the radicand or simplify it to i in your first step. Both are correct.

Example 4

Simplify.

$\sqrt{–12}$

Example 5