Square Root Calculator
Calculate the square root of any number instantly, including both positive and negative inputs. For positive numbers, the calculator returns the principal (non-negative) real root. For negative numbers, it returns the complex result using imaginary number notation (i). The calculator also provides the squared verification so you can confirm the answer.
Enter Values
Result
Enter values above and click Calculate to see your result.
AI Assistant
Ask about this calculator
I can help you understand the square root calculator formula, interpret your results, and answer follow-up questions.
Try asking
Formula
How it works: For n >= 0, the square root is the non-negative number that, when multiplied by itself, equals n. For example, sqrt(49) = 7 because 7 x 7 = 49. For n < 0, the result is expressed as i x sqrt(|n|), where i is the imaginary unit representing sqrt(-1).
Worked Example
Frequently Asked Questions
Can this calculate square roots of negative numbers?
Yes. Negative inputs produce complex (imaginary) results. For example, sqrt(-49) = 7i, where i is the imaginary unit. This is useful in electrical engineering, physics, and advanced mathematics.
How do I verify the result?
Square the result and confirm it equals your original number. For example, if sqrt(49) = 7, then 7 x 7 = 49 confirms the answer. The calculator shows this verification automatically.
What is the square root of 0?
The square root of 0 is 0, because 0 x 0 = 0. Zero is the only number that is its own square root alongside 1.
Are all square roots irrational?
No. Perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100...) have whole number square roots. Non-perfect squares like 2, 3, 5, 7 have irrational square roots that continue infinitely without repeating.
What is the difference between sqrt and cube root?
Square root finds a number that multiplied by itself gives the original. Cube root finds a number that multiplied by itself three times gives the original. For example, sqrt(9) = 3 but cbrt(27) = 3.
How can I put this Square Root Calculator on my blog or website?
Yes, the Square Root Calculator is fully embeddable. Tap "Embed" above to configure appearance and copy the code. It is free to use, works on any platform (HTML, WordPress, CMS), and adjusts to any screen size automatically. Visit calculory.com/services/embed-calculators for the complete guide.
AI Assistant
Ask about this calculator
I can help you understand the square root calculator formula, interpret your results, and answer follow-up questions.
Try asking
Related Calculators
More Maths Calculators
View allRelated Articles
All articles
Types of Calculators in 2026: A Complete Guide to Choosing the Right One
Every type of calculator explained: basic, desk, scientific, graphing, printing, financial, construction (Sonic Cal style), online, app, and voice. Pick the right one in under a minute.
Read article
Best Voice Calculators in 2026: Online Tools and Mobile Apps Compared
The best voice calculators of 2026 compared: web tools, iPhone and Android apps, talking calculators, and PC options. Find the right voice activated calculator.
Read article
Best Math Training Apps in 2026: 12 Picks for Students, Adults, and Speed Enthusiasts
We tested 12 math training apps across four categories: academic support, logical reasoning, mental math speed, and gamified learning. See which apps actually improve your skills in 2026.
Read article
Guide to Interactive Math Games for Kids and Classrooms 2026
Interactive math games in 2026 blend adaptive online platforms with low-prep classroom activities. Use this guide to pick the best game format by age, goal, and time.
Read articleModern Tools for Every Need
Accurate and Reliable
All calculations run locally. Step-by-step solutions you can trust.
Verified Precision
Precise Mathematical Calculations Powered by Calculory AI