Principal Square Root of a Negative Number
For any positive real number
This follows from
Quick Reference
| Expression | Value | Reasoning |
|---|---|---|
| Definition: |
||
Definition
Since
Definition. The principal square root of
For any positive real number
For example:
Example 1. Simplify
Solution.
A Critical Warning: Products of Negative Square Roots
For positive numbers
Warning. The product rule
The correct result is
Example 2. Compute
Correct approach:
Incorrect approach (do not use):
The correct answer is
Example 3. Simplify
Solution.
Alternatively,
Simplifying Expressions with
When simplifying expressions involving square roots of negative numbers, always convert to the
Example 4. Compute
Solution. Convert first:
