Calculate sixth roots from integers, simplify exact forms, find complex roots for negatives, or enter y to compute y⁶ and verify the result.

Real sixth root means the non-negative principal root. Negative inputs require complex mode. Exact simplification accepts whole numbers up to 1 trillion.

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Sixth Root Formula

The following two example problems outline the steps and information needed to calculate the Sixth Root.

6R = X ^ (1 / 6)

Variables:

  • 6R is the Sixth Root
  • X is a non-negative real number for the principal real sixth root. Negative inputs have complex roots; exact simplification requires an integer.

How to Calculate Sixth Root?

The following steps outline how to calculate the Sixth Root.

  1. First, choose the calculation mode. Enter x to find its principal sixth root, or y to compute y⁶; the principal sixth root of y⁶ is |y|.
  2. Next, gather the formula from above: 6R = X ^ (1/6).
  3. Finally, calculate the Sixth Root.
  4. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

any integer = 50

6R = 50^(1/6) ≈ 1.919383. Exact form is ⁶√50. For nonzero real x, complex roots use |x|^(1/6) cis((arg x + 2πk)/6), k = 0,…,5.