Square Root Calculator
Calculate square roots and other whole-number roots.
How do I find a square root?
The square root of a number is the value that gives the number when multiplied by itself.
Formula: The nth root of x is x^(1/n). Negative numbers have real roots only for odd integer indices.
Square root
9
- Check
- 9 ^ 2 = 81
What this calculator does
Find square, cube, and higher roots with real-number validation for negative values.
Use it to turn Number, Root index into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this math calculation.
Inputs and what they mean
- Number
- — number value.
- Root index
- — number value.
How to use it
- Enter the requested values.
- Choose the calculation mode when available.
- Review the result and supporting breakdown.
Formula
The nth root of x is x^(1/n). Negative numbers have real roots only for odd integer indices.
Inputs used: Number, Root index.
Edge handling: Number is required.; Root index is required.; Root index must be greater than zero..
Worked example
Square root of 81
- Start with Number: 81, Root index: 2.
- Apply the method: The nth root of x is x^(1/n). Negative numbers have real roots only for odd integer indices.
- √81 = 9.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this square root calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Common questions
How do I find a square root?
The square root of a number is the value that gives the number when multiplied by itself. Check the formula, example, and limitations on this page before using the result for a real math decision.
Can I calculate cube roots?
Yes. Set the root index to 3.
Can I use negative numbers?
Yes for odd roots, such as the cube root of −8. Check the formula, example, and limitations on this page before using the result for a real math decision.
How do I use the Square Root Calculator?
Enter the required values for Number, Root index. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Square Root Calculator use?
The nth root of x is x^(1/n). Negative numbers have real roots only for odd integer indices. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Can the Square Root Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Cite this page
Free Calculator. (n.d.). Square Root Calculator. https://freecalculator.tech/tools/square-root-calculator
"Square Root Calculator." Free Calculator, https://freecalculator.tech/tools/square-root-calculator.
Square Root Calculator — Free Calculator, https://freecalculator.tech/tools/square-root-calculator
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