Root Calculator
Compute the nth root of x for any degree n ≥ 2. Odd roots of negative numbers work correctly, even roots of negatives are caught with a clear explanation, and a table compares the square, cube and higher roots of the same input.
TheCalculators — Root Calculator
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3th root of 27
3
|27|^(1/3) · check: 3^3 ≈ 27
- Radicand (x)
- 27
- Degree (n)
- 3
- Root
- 3
- As fractional exponent
- 27^(1/3)
- Check
- 3^3 = 27 ≈ x ✓
- Root type
- Odd root — sign is preserved
- Square root
- 5.19615242
- Cube root
- 3
Step-by-step
- 1Write as a fractional exponentⁿ√x = x^(1/n) → 27^(1/3)
- 2Handle the signn = 3 is odd, so a negative radicand keeps its sign: root(−|x|) = −root(|x|). |x| = 27.
- 3Evaluate(27)^(1/3) = 3
- 4Verify3^3 = 27 ≈ 27 ✓
All real roots of 27 (degrees 2–9)
Values are rounded to 8 decimal places; irrational roots (like √2) cannot be written exactly.
Most useful next
Formula
ⁿ√x = x^(1/n); odd n allows x < 0, even n requires x ≥ 0
Pro tips
- • Roots are fractional exponents: the cube root of x is x^(1/3), which makes mixed powers like x^(5/2) = √(x⁵) easy.
- • A quick sanity check: raise your answer back to the nth power — you should get the original number.
- • For even degrees, negative radicands need complex numbers; the calculator blocks them with an explanation.
FAQ
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