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n-th Root of a Number

Calculate the n-th root of a non-negative number using x^(1/n).

Author

Prof. Sunita Rao

Math editorial contributor

Indian-American chemical engineer at Stanford, developing biodegradable alternatives to single-use plastics

Reviewed by

Dr. Emeka Nwosu

Math content reviewer

Nigerian legal scholar with an SJD from Yale, focused on international trade law and African continental free trade agreements

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

Table of Contents

  1. Reference values
  2. Calculator
  3. Reference table
  4. FAQs
  5. Methodology and review
  6. Related conversions

27 Value Value; 2 Root Index (n) Root Index (n) =

5.196152 Root Value

Representative value from the n-th Root of a Number reference table.

Reference Values

Browse 126 reference values with individual detail pages for quick lookup.

Browse all reference values

n-th Root of a Number

Calculate the n-th root of a non-negative number using x^(1/n).

Calculated Result

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Reference Table

Use this complete table for quick lookup and internal linking to specific value pages.

n-th Root of a Number Reference
Scenarion-th Root
0 Value Value; 2 Root Index (n) Root Index (n)0 Root Value
0 Value Value; 3 Root Index (n) Root Index (n)0 Root Value
0 Value Value; 4 Root Index (n) Root Index (n)0 Root Value
0 Value Value; 5 Root Index (n) Root Index (n)0 Root Value
0 Value Value; 6 Root Index (n) Root Index (n)0 Root Value
0 Value Value; 8 Root Index (n) Root Index (n)0 Root Value
0 Value Value; 10 Root Index (n) Root Index (n)0 Root Value
0.125 Value Value; 2 Root Index (n) Root Index (n)0.353553 Root Value
0.125 Value Value; 3 Root Index (n) Root Index (n)0.5 Root Value
0.125 Value Value; 4 Root Index (n) Root Index (n)0.594604 Root Value
0.125 Value Value; 5 Root Index (n) Root Index (n)0.659754 Root Value
0.125 Value Value; 6 Root Index (n) Root Index (n)0.707107 Root Value
0.125 Value Value; 8 Root Index (n) Root Index (n)0.771105 Root Value
0.125 Value Value; 10 Root Index (n) Root Index (n)0.812252 Root Value
0.25 Value Value; 2 Root Index (n) Root Index (n)0.5 Root Value
0.25 Value Value; 3 Root Index (n) Root Index (n)0.629961 Root Value
0.25 Value Value; 4 Root Index (n) Root Index (n)0.707107 Root Value
0.25 Value Value; 5 Root Index (n) Root Index (n)0.757858 Root Value
0.25 Value Value; 6 Root Index (n) Root Index (n)0.793701 Root Value
0.25 Value Value; 8 Root Index (n) Root Index (n)0.840896 Root Value
0.25 Value Value; 10 Root Index (n) Root Index (n)0.870551 Root Value
0.5 Value Value; 2 Root Index (n) Root Index (n)0.707107 Root Value
0.5 Value Value; 3 Root Index (n) Root Index (n)0.793701 Root Value
0.5 Value Value; 4 Root Index (n) Root Index (n)0.840896 Root Value
0.5 Value Value; 5 Root Index (n) Root Index (n)0.870551 Root Value
0.5 Value Value; 6 Root Index (n) Root Index (n)0.890899 Root Value
0.5 Value Value; 8 Root Index (n) Root Index (n)0.917004 Root Value
0.5 Value Value; 10 Root Index (n) Root Index (n)0.933033 Root Value
1 Value Value; 2 Root Index (n) Root Index (n)1 Root Value
1 Value Value; 3 Root Index (n) Root Index (n)1 Root Value
1 Value Value; 4 Root Index (n) Root Index (n)1 Root Value
1 Value Value; 5 Root Index (n) Root Index (n)1 Root Value
1 Value Value; 6 Root Index (n) Root Index (n)1 Root Value
1 Value Value; 8 Root Index (n) Root Index (n)1 Root Value
1 Value Value; 10 Root Index (n) Root Index (n)1 Root Value
2 Value Value; 2 Root Index (n) Root Index (n)1.414214 Root Value
2 Value Value; 3 Root Index (n) Root Index (n)1.259921 Root Value
2 Value Value; 4 Root Index (n) Root Index (n)1.189207 Root Value
2 Value Value; 5 Root Index (n) Root Index (n)1.148698 Root Value
2 Value Value; 6 Root Index (n) Root Index (n)1.122462 Root Value
2 Value Value; 8 Root Index (n) Root Index (n)1.090508 Root Value
2 Value Value; 10 Root Index (n) Root Index (n)1.071773 Root Value
4 Value Value; 2 Root Index (n) Root Index (n)2 Root Value
4 Value Value; 3 Root Index (n) Root Index (n)1.587401 Root Value
4 Value Value; 4 Root Index (n) Root Index (n)1.414214 Root Value
4 Value Value; 5 Root Index (n) Root Index (n)1.319508 Root Value
4 Value Value; 6 Root Index (n) Root Index (n)1.259921 Root Value
4 Value Value; 8 Root Index (n) Root Index (n)1.189207 Root Value
4 Value Value; 10 Root Index (n) Root Index (n)1.148698 Root Value
8 Value Value; 2 Root Index (n) Root Index (n)2.828427 Root Value
8 Value Value; 3 Root Index (n) Root Index (n)2 Root Value
8 Value Value; 4 Root Index (n) Root Index (n)1.681793 Root Value
8 Value Value; 5 Root Index (n) Root Index (n)1.515717 Root Value
8 Value Value; 6 Root Index (n) Root Index (n)1.414214 Root Value
8 Value Value; 8 Root Index (n) Root Index (n)1.29684 Root Value
8 Value Value; 10 Root Index (n) Root Index (n)1.231144 Root Value
16 Value Value; 2 Root Index (n) Root Index (n)4 Root Value
16 Value Value; 3 Root Index (n) Root Index (n)2.519842 Root Value
16 Value Value; 4 Root Index (n) Root Index (n)2 Root Value
16 Value Value; 5 Root Index (n) Root Index (n)1.741101 Root Value
16 Value Value; 6 Root Index (n) Root Index (n)1.587401 Root Value
16 Value Value; 8 Root Index (n) Root Index (n)1.414214 Root Value
16 Value Value; 10 Root Index (n) Root Index (n)1.319508 Root Value
27 Value Value; 2 Root Index (n) Root Index (n)5.196152 Root Value
27 Value Value; 3 Root Index (n) Root Index (n)3 Root Value
27 Value Value; 4 Root Index (n) Root Index (n)2.279507 Root Value
27 Value Value; 5 Root Index (n) Root Index (n)1.933182 Root Value
27 Value Value; 6 Root Index (n) Root Index (n)1.732051 Root Value
27 Value Value; 8 Root Index (n) Root Index (n)1.509804 Root Value
27 Value Value; 10 Root Index (n) Root Index (n)1.390389 Root Value
32 Value Value; 2 Root Index (n) Root Index (n)5.656854 Root Value
32 Value Value; 3 Root Index (n) Root Index (n)3.174802 Root Value
32 Value Value; 4 Root Index (n) Root Index (n)2.378414 Root Value
32 Value Value; 5 Root Index (n) Root Index (n)2 Root Value
32 Value Value; 6 Root Index (n) Root Index (n)1.781797 Root Value
32 Value Value; 8 Root Index (n) Root Index (n)1.542211 Root Value
32 Value Value; 10 Root Index (n) Root Index (n)1.414214 Root Value
64 Value Value; 2 Root Index (n) Root Index (n)8 Root Value
64 Value Value; 3 Root Index (n) Root Index (n)4 Root Value
64 Value Value; 4 Root Index (n) Root Index (n)2.828427 Root Value
64 Value Value; 5 Root Index (n) Root Index (n)2.297397 Root Value
64 Value Value; 6 Root Index (n) Root Index (n)2 Root Value
64 Value Value; 8 Root Index (n) Root Index (n)1.681793 Root Value
64 Value Value; 10 Root Index (n) Root Index (n)1.515717 Root Value
81 Value Value; 2 Root Index (n) Root Index (n)9 Root Value
81 Value Value; 3 Root Index (n) Root Index (n)4.326749 Root Value
81 Value Value; 4 Root Index (n) Root Index (n)3 Root Value
81 Value Value; 5 Root Index (n) Root Index (n)2.408225 Root Value
81 Value Value; 6 Root Index (n) Root Index (n)2.080084 Root Value
81 Value Value; 8 Root Index (n) Root Index (n)1.732051 Root Value
81 Value Value; 10 Root Index (n) Root Index (n)1.551846 Root Value
125 Value Value; 2 Root Index (n) Root Index (n)11.18034 Root Value
125 Value Value; 3 Root Index (n) Root Index (n)5 Root Value
125 Value Value; 4 Root Index (n) Root Index (n)3.343702 Root Value
125 Value Value; 5 Root Index (n) Root Index (n)2.626528 Root Value
125 Value Value; 6 Root Index (n) Root Index (n)2.236068 Root Value
125 Value Value; 8 Root Index (n) Root Index (n)1.828579 Root Value
125 Value Value; 10 Root Index (n) Root Index (n)1.620657 Root Value
256 Value Value; 2 Root Index (n) Root Index (n)16 Root Value
256 Value Value; 3 Root Index (n) Root Index (n)6.349604 Root Value
256 Value Value; 4 Root Index (n) Root Index (n)4 Root Value
256 Value Value; 5 Root Index (n) Root Index (n)3.031433 Root Value
256 Value Value; 6 Root Index (n) Root Index (n)2.519842 Root Value
256 Value Value; 8 Root Index (n) Root Index (n)2 Root Value
256 Value Value; 10 Root Index (n) Root Index (n)1.741101 Root Value
512 Value Value; 2 Root Index (n) Root Index (n)22.627417 Root Value
512 Value Value; 3 Root Index (n) Root Index (n)8 Root Value
512 Value Value; 4 Root Index (n) Root Index (n)4.756828 Root Value
512 Value Value; 5 Root Index (n) Root Index (n)3.482202 Root Value
512 Value Value; 6 Root Index (n) Root Index (n)2.828427 Root Value
512 Value Value; 8 Root Index (n) Root Index (n)2.181015 Root Value
512 Value Value; 10 Root Index (n) Root Index (n)1.866066 Root Value
1,000 Value Value; 2 Root Index (n) Root Index (n)31.622777 Root Value
1,000 Value Value; 3 Root Index (n) Root Index (n)10 Root Value
1,000 Value Value; 4 Root Index (n) Root Index (n)5.623413 Root Value
1,000 Value Value; 5 Root Index (n) Root Index (n)3.981072 Root Value
1,000 Value Value; 6 Root Index (n) Root Index (n)3.162278 Root Value
1,000 Value Value; 8 Root Index (n) Root Index (n)2.371374 Root Value
1,000 Value Value; 10 Root Index (n) Root Index (n)1.995262 Root Value
4,096 Value Value; 2 Root Index (n) Root Index (n)64 Root Value
4,096 Value Value; 3 Root Index (n) Root Index (n)16 Root Value
4,096 Value Value; 4 Root Index (n) Root Index (n)8 Root Value
4,096 Value Value; 5 Root Index (n) Root Index (n)5.278032 Root Value
4,096 Value Value; 6 Root Index (n) Root Index (n)4 Root Value
4,096 Value Value; 8 Root Index (n) Root Index (n)2.828427 Root Value
4,096 Value Value; 10 Root Index (n) Root Index (n)2.297397 Root Value

Frequently Asked Questions

Common questions about n-th Root of a Number, formulas, and typical use cases.

What does the n-th Root of a Number calculator do?

It helps with computing square roots, cube roots, and higher-order roots in algebra and engineering math.

What formula does the n-th Root of a Number calculator use?

n-th root = x^(1/n).

What inputs are valid?

Value must be non-negative, and the root index n must be a positive integer.

When would I use this?

computing square roots, cube roots, and higher-order roots in algebra and engineering math

Methodology and Review

This page combines a live calculator, precomputed reference values, and FAQ content from the same conversion definition to reduce mismatch between calculator output and lookup tables.

Editorial metadata (author, reviewer, and update date) is rendered on the page and in structured data. See our editorial policy, review process, and corrections policy.

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