1. What is Sixth Root?

The sixth root of a number is a value that, when multiplied by itself six times, gives the original number. It is the inverse operation of raising a number to the power of 6.

2. How Does the Calculator Work?

The calculator uses the sixth root formula:

Where:

• \( a \) — Any non-negative real number

Explanation: The sixth root is calculated by raising the number to the power of 1/6.

3. Mathematical Explanation

Details: For positive real numbers, there is exactly one positive real sixth root. For zero, the sixth root is zero. Negative numbers have complex sixth roots.

4. Using the Calculator

Tips: Enter any non-negative number to calculate its sixth root. The calculator will return the principal (real) sixth root.

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate sixth roots of negative numbers?
A: Negative numbers have complex sixth roots (with imaginary components), which this calculator doesn't display.

Q2: What's the sixth root of zero?
A: The sixth root of zero is zero (0).

Q3: How precise is this calculation?
A: The calculator provides results rounded to 6 decimal places.

Q4: What's the relationship between sixth root and cube root?
A: The sixth root can be expressed as the square root of the cube root: \( \sqrt[6]{a} = \sqrt{\sqrt[3]{a}} \).

Q5: Are sixth roots used in real-world applications?
A: Yes, sixth roots appear in various engineering, physics, and statistical calculations, particularly in equations involving volume scaling or wave functions.