Root calculator
Index n from 2 to 20; radicand can be an integer, decimal, fraction, e or pi.
Convention: for a positive radicand, ⁿ√a means the principal nonnegative real root. If a<0 and n is odd, the principal real root is negative. If a<0 and n is even, there is no real root, so the principal complex root is shown.
Result
Ready to calculate.
principal root
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Decimal
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Real solutions xⁿ=a
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Complex roots
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Verification
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Calculation steps appear here.
All roots appear after calculation.
Key facts:
ⁿ√a = a^(1/n).
If n is even and a>0, xⁿ=a has two real solutions ±ⁿ√a.
If n is odd, xⁿ=a has one real solution.
Over the complex numbers, every nonzero a has exactly n distinct nth roots: |a|^(1/n)·cis((arg a + 2πk)/n), k=0,…,n−1.
ⁿ√a = a^(1/n).
If n is even and a>0, xⁿ=a has two real solutions ±ⁿ√a.
If n is odd, xⁿ=a has one real solution.
Over the complex numbers, every nonzero a has exactly n distinct nth roots: |a|^(1/n)·cis((arg a + 2πk)/n), k=0,…,n−1.