√ Square Root Calculator
Calculate square roots and nth roots
How Square Root Calculation Works
Formula
√n = n^(1/2)
- 1Enter the number you want to find the root of.
- 2Select the root type: square root (2), cube root (3), or custom (n).
- 3The calculator computes the root using exponentiation.
- 4If the result is a perfect root, it's shown as a whole number.
- 5Non-perfect roots show the simplified radical form and decimal approximation.
About Square Root Calculator
Calculate square roots, cube roots, and nth roots of any number. Shows step-by-step simplification, perfect square detection, and radical form. Handles positive and negative inputs.
Frequently Asked Questions
Can you take the square root of a negative number?
Not in real numbers. The square root of a negative number involves imaginary numbers (i = √−1). For example, √−16 = 4i. Cube roots of negative numbers are real: ∛−8 = −2.
What is a perfect square?
A perfect square is a number whose square root is a whole number. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. The number 144 is 12², making it a perfect square.
How do I simplify a square root?
Factor out perfect squares from under the radical. For example, √72 = √(36 × 2) = 6√2. Find the largest perfect square factor and take its root outside the radical sign.