Square Root Calculator
Calculate square roots and simplify radicals, e.g. √72 = 6√2, and check whether a number is a perfect square.
Your inputs
Results
√72
8.48528137424
- Simplified radical form
- 6√2
- Perfect square?
- No
- Check: result^2
- 72
✓Exact calculation — rounded only for display
What this calculator does
Besides the decimal value, simplified radical form is useful in algebra and geometry.
Formula and method
√n = a√b where n = a² × b and b has no square factor (found by prime factorization).
Worked example
Calculated by this tool with its default inputs:
Inputs
- Number: 72
Results
- √72: 8.48528137424
- Simplified radical form: 6√2
- Perfect square?: No
- Check: result^2: 72
How to read the results
If b = 1, the number is a perfect square.
Assumptions and limitations
- Negative numbers have no real square root.
Questions
Why simplify radicals?
Exact forms avoid rounding and make algebra easier.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy