Square Root Calculator
Calculate square roots, cube roots, and nth roots of any number instantly.
How to Use
- Enter any non-negative number in the input field.
- Optionally change the nth root value (default is 2 for square root).
- Click "Calculate" to see the square root, cube root, and more.
How It Works
The square root of a number x is the value that, when multiplied by itself, equals x. For example, √144 = 12 because 12 × 12 = 144. A perfect square is a number whose square root is a whole number. The nth root generalizes this concept: the nth root of x is x raised to the power of 1/n.
What Is a Square Root?
The square root of a number is the value that, when multiplied by itself, produces the original number. For example, the square root of 49 is 7, because 7 × 7 = 49. The concept extends naturally to cube roots (what number multiplied by itself three times gives you the original?) and nth roots for any positive integer n.
Square roots come up constantly in geometry, physics, engineering, and finance. You need them to calculate distances (the Pythagorean theorem), find the side length of a square with a known area, compute standard deviations in statistics, and much more. This calculator gives you the square root, cube root, and any nth root you need, plus it tells you whether the input is a perfect square — all in one click.
Frequently Asked Questions
What is a perfect square?
A perfect square is a number whose square root is a whole number. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. If you take the square root and get a decimal, the number is not a perfect square. This calculator automatically checks this for you.
Can I calculate the square root of a negative number?
Not with this tool. The square root of a negative number involves imaginary numbers (denoted with "i"), which are part of the complex number system. For example, the square root of -9 is 3i. This calculator works with real numbers only, so it requires non-negative input.
What is an nth root?
The nth root of a number x is the value that, when raised to the power n, equals x. A square root is a 2nd root, a cube root is a 3rd root, and so on. Mathematically, the nth root of x equals x raised to the power of 1/n. This calculator lets you compute any nth root by changing the root value.
How precise are the results?
Results are rounded to 5 decimal places, which provides more than enough precision for most practical applications. Keep in mind that many square roots are irrational numbers (like the square root of 2 = 1.41421...) that go on forever without repeating, so some rounding is always necessary.
What does the "squared" result show?
The squared result shows your input number multiplied by itself. This is the inverse operation of a square root. It's included as a quick reference — for example, if you enter 12, you'll see that 12 squared is 144, which confirms that the square root of 144 is 12.
Example Calculation
Scenario: You have a square garden with an area of 225 square feet and want to know the length of each side.
Step 1:Enter 225 in the input field and click "Calculate."
Step 2: The square root result shows 15, meaning each side of the garden is 15 feet long.
Step 3:The calculator also confirms 225 is a "Perfect Square" (Yes), since 15 is a whole number.
Bonus: The cube root of 225 is approximately 6.08252 (the side length of a cube with volume 225), and 225 squared is 50,625.