Square Root Calculator

Calculate square and nth roots

About the Calculator

Roots show up in algebra, geometry, and real world formulas, but the math can be slow without a calculator. This tool finds square roots and any nth root quickly, so you can focus on solving the bigger problem. Use it for homework, engineering formulas, or quick checks in class or at work. It also helps you see the difference between perfect squares and irrational results. Enter a number, set the root you want, and get an immediate answer. It is a simple way to keep your work accurate without breaking your flow. Use the Square Root Calculator to get a clear result you can act on right away.

Number

Root TypeSquare Root

Square Root

Verification: 12^2 = 144

The Formula

√n = n^(1/2) | ∛n = n^(1/3) | ⁿ√x = x^(1/n)

How to Calculate Manually

1
For square roots, find a number that multiplied by itself equals your number.
2
For other roots, find a number that when raised to that power equals your number.
3
Use prime factorization to simplify roots of large numbers.
4
Perfect squares have whole number square roots.
5
Most numbers have irrational (non-repeating decimal) roots.

Examples

What is √144?

12 (because 12 × 12 = 144)

What is ∛27?

3 (because 3 × 3 × 3 = 27)

What is √50?

≈ 7.071 (or 5√2 in simplified radical form)

💡 Tips

•Perfect squares to memorize: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
•√(a×b) = √a × √b - useful for simplifying.
•Negative numbers don't have real square roots (but do have imaginary roots).
•Cube roots of negative numbers are negative.

🎉 Fun Facts

•√2 Broke Greek Mathematics: Around 500 BC, Pythagoreans discovered √2 = 1.41421356... is irrational (never-ending, non-repeating decimals), shattering their belief that all numbers were fractions and allegedly causing mathematician Hippasus to be drowned for revealing it.
•Pythagorean Theorem Everywhere: The formula a² + b² = c² (requiring square roots) is used millions of times daily in GPS navigation, construction, video game graphics, and even determining baseball diamond distances, making it perhaps the most-used math theorem in modern life.
•The Symbol's Typography Origin: The square root symbol √ was introduced in 1525 by mathematician Christoph Rudolff and comes from a stylized lowercase 'r' (for "radix" meaning root in Latin); it's essentially a 500-year-old abbreviation.
•Sprint Speed Square Root: Your maximum running speed is roughly proportional to the square root of your leg length; which is why horses (√100cm ≈ 10) run faster than humans (√90cm ≈ 9.5), despite having only 11% longer legs.
•Inverse Square Law: Light intensity decreases by the square of distance; so a lamp 2 feet away is ¼ as bright as at 1 foot (1/2² = 1/4), and at 3 feet it's 1/9 as bright (1/3² = 1/9), explaining why rooms get dark so quickly.
•Video Game Distance Formula: Every video game uses √(Δx² + Δy²) millions of times per second to calculate distances between characters, bullets, and objects; without square roots, 3D games wouldn't exist.