How do you solve sqrt(x+3) + 5 = 0 and find any extraneous solutions?

Mar 5, 2017

This equation has no solutions.

Explanation:

Note that for any Real value of $x$ one of the following holds:

• $x + 3 \ge 0 \text{ }$ and $\text{ } \sqrt{x + 3} \ge 0$

• $x + 3 < 0 \text{ }$ and $\text{ "sqrt(x+3) = (sqrt(-x-3))i" }$ is pure imaginary with positive imaginary part.

In particular $\sqrt{x + 3}$ cannot be a negative Real number if $x$ is Real.

Hence the given equation has no Real solution.