Radical Arithmetic Calculator
Add, subtract, multiply or divide two real radical terms. Simplify square factors, combine matching radicals and rationalize a radical denominator.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Simplify each square root to a square-free radicand. Add coefficients only when the simplified radicands match. For division, multiply by the denominator radical to remove it from the denominator.
a√m ÷ b√n = a√(mn)/(bn), for b√n≠0
Worked example
2√8+√18=4√2+3√2=7√2. Also √2/√3=√6/3.
Assumptions and input details
Fractions and decimals up to six places are accepted, with input magnitude at most1e6 and reduced denominator at most1e6. Exact fractions determine the result; decimal displays and diagrams are rounded. Radicands must be integers from0 to1e6. Negative coefficients are allowed; negative radicands are not real in this tool.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Integer and fraction results are exact within the documented limits. Radical decimal values and plotted interval positions are approximate.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Simplify a real square root into a√b, with prime-factor pairs and a decimal check. Distinguish the principal square root from both solutions of x²=n.
Add, subtract, multiply or divide fractions and mixed numbers. Follow exact fraction steps, simplification and a number-line diagram.
Add, subtract, multiply or divide two complex numbers. Enter real and imaginary parts separately, then inspect magnitude, argument and an equal-scale complex-plane diagram.
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