College Algebra / Unit 4 Alg 190 short lesson, about 20 seconds
Square Roots of Negative Numbers
Captions available
The idea
The principal square root of a negative number is imaginary: √(−a) = i√a for positive a.
In practice
√(−9) = 3i, and the check squares back: (3i)² = 9i² = −9. The radical now answers every real input.
Where people slip
Factor the −1 out as i before touching anything else.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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