How to use this calculator
- Enter or choose number.
- Enter or choose root index (n).
- The root updates as you type. Use Copy result or Share to keep it.
Method
ⁿ√x = x^(1/n); simplify by taking out every prime factor that appears n times: √(k²·m) = k√m
- x
- the radicand
- n
- the index of the root
Worked example
- 72 = 2³ × 3² = (2 × 3)² × 2 = 36 × 2.
- √72 = √36 × √2 = 6√2.
- 6 × 1.41421356 = 8.4852813742.
The square root of 72 is 6√2, about 8.4853.
What the result means
The simplified radical is exact; the decimal is rounded to 10 places. A number with an exact whole-number root (64 for square and cube roots) is a perfect power.
Assumptions and limits
- Only real roots are returned: the principal (positive) root for even n.
- Simplified radicals are shown for whole numbers only.
- Complex roots of negative numbers are not covered.
Questions
Why is there no square root of −4?
No real number squared is negative. The answer is the imaginary number 2i, which this calculator does not cover.
Does 25 have two square roots?
Yes, 5 and −5. The √ symbol means the principal (non-negative) root, 5.