Square Root Calculator
Square root, cube root, or any nth root — with simplified radical form
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Quick summary
Enter a number to find its square root, or set the root degree for a cube root (3) or any nth root. √144 = 12, and it flags perfect powers. For non-perfect squares, it also gives the simplified radical form by pulling out the largest perfect-square factor — √12 = 2√3. Odd roots (like cube roots) work for negative numbers too: ∛−8 = −2.
Reviewed by Simple Calculators TeamLast reviewed
How to use this calculator
- Enter the inputs requested by the calculator.
- Choose the units or options that match your situation and review the assumptions.
- Run or update the calculation to see the result.
- Review the result, breakdown, and formulas shown on the page.
- Check the inputs, units, dates, and limitations before saving or sharing the result.
Frequently asked questions
How do I calculate a square root?
The square root of a number is the value that, multiplied by itself, gives the number — √144 = 12 because 12 × 12 = 144. For non-perfect squares the root is irrational (√2 ≈ 1.414). This calculator gives the decimal value and, for square roots, a simplified radical form.
How do I simplify a square root?
Pull out the largest perfect-square factor. For √12, the largest perfect square dividing 12 is 4, so √12 = √4 × √3 = 2√3. This 'simplified radical' form is exact, unlike a rounded decimal. The calculator does the factoring automatically for square roots.
Can I find cube roots and other roots?
Yes — set the root degree. Degree 2 is the square root, 3 is the cube root, and so on up to 20. The nth root of a number is the value that, raised to the nth power, returns it: ∛27 = 3 because 3³ = 27.
Can you take the root of a negative number?
Odd roots (cube root, 5th root, …) of negatives are real: ∛−8 = −2. Even roots (square root, 4th root, …) of a negative number have no real value — they're imaginary — so the calculator flags those cases.
Key terms
- Square Root
- A value that, squared, gives the number; √144 = 12.
- Radicand
- The number under the radical sign.
- Simplified Radical
- Exact form with the largest perfect square pulled out, e.g. 2√3.
- Perfect Square
- A number whose square root is a whole number (4, 9, 16…).
Methodology, sources & limitations
This page shows the formula, assumptions, and limitations used for this estimate. Rates, thresholds, and other time-sensitive inputs can change, so verify them against the relevant official source before relying on a result.
For our review approach and the primary sources we consult, see the methodology and source policy. If you spot an outdated figure or formula, please contact us with a correction.