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Nth Root Calculator

Number

Root (n)

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What is Nth Root Calculator?

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The nth root of a number x is the value r such that rⁿ = x. The square root is the 2nd root; cube root is the 3rd root. For even roots of negative numbers, no real solution exists (result is a complex number).

PrimeCalcPro provides professional-grade tools trusted by businesses and academics.

Τύπος

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f(x)ⁿ√x = x^(1/n)

Variable Legend

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Σύμβολο	Όνομα	Μονάδα	Περιγραφή
x	x^(1/3)	—	x^(1/3)

How to Nth Root Calculator

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1ⁿ√x = x^(1/n)
2Square root: ²√x = x^0.5
3Cube root: ³√x = x^(1/3)
4Nth root: use x^(1/n) on a calculator
5Negative numbers: odd roots are fine (³√−8 = −2); even roots are complex

Worked Examples

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Example 1

Given:4th root of 81

Αποτέλεσμα:3

3⁴ = 81 → ⁴√81 = 3

Example 2

Given:5th root of 32

Αποτέλεσμα:2

2⁵ = 32 → ⁵√32 = 2

Example 3

Given:Cube root of 125

Αποτέλεσμα:5

5³ = 125

Real-World Applications

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Academic homework and exam preparation

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Engineering and architecture calculations

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Everyday measurement tasks around the home

Frequently Asked Questions

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What is Nth Root?

The nth root of a number x is the value r such that rⁿ = x. The square root is the 2nd root; cube root is the 3rd root

How accurate is the Nth Root calculator?

The calculator uses the standard published formula for nth root. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Nth Root calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Nth Root calculator use?

The core formula is: ⁿ√x = x^(1/n). Each step in the calculation is shown so you can verify the result manually.

References

Mathematically verified

Reviewed October 2026

Our methodology

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Nth Root Calculator