Root Calculator
Calculate square roots, cube roots, and nth roots of any number. Shows decimal result and identifies perfect powers.
Square Root
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Exact Form
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Perfect Power
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What is Root Calculator?
The root calculator computes square roots, cube roots, and nth roots of any number. It also identifies whether the result is a perfect power and displays simplified exact forms when applicable.
How to use
- 1 Enter the number you want to find the root of.
- 2 Select the root type: square root (2nd), cube root (3rd), or nth root.
- 3 If you selected nth root, enter the degree (e.g. 4 for a 4th root).
- 4 Click Calculate to see the result.
- 5 The calculator shows decimal result and whether the input is a perfect power.
Formula
Example calculation
Square root of 144 = 12 (perfect square). Cube root of 27 = 3 (perfect cube). 4th root of 256 = 4 (perfect 4th power). Square root of 2 ≈ 1.41421356.
Frequently asked questions
What is a perfect square?
A perfect square is an integer whose square root is also an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Can you take the square root of a negative number?
Not in the real number system. The square root of a negative number is imaginary (uses the complex unit i). This calculator works with real numbers only.
What is the difference between a root and an exponent?
They are inverse operations. Taking the nth root of x is the same as raising x to the power 1/n. For example, √9 = 9^(1/2) = 3.
What is an irrational root?
Most roots are irrational — they cannot be expressed as a simple fraction. For example, √2 ≈ 1.41421356... continues infinitely without repeating.
How is the cube root different from the square root?
The square root finds a number that when squared gives the original. The cube root finds a number that when cubed gives the original. Cube roots of negative numbers are real (e.g., ∛(−8) = −2).