1. What is a Sixth Root?

The sixth root of a number x is a value that, when multiplied by itself six times, gives the original number x. Mathematically, it's represented as \( \sqrt[6]{x} \) or \( x^{1/6} \).

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( x \) — The number you want to find the sixth root of
• The exponent \( \frac{1}{6} \) represents the sixth root operation

3. Mathematical Explanation

Details: In real numbers, sixth roots only exist for non-negative numbers. For negative numbers, the sixth root would be complex and isn't calculated by this tool.

The sixth root function is the inverse of raising a number to the sixth power:

4. Using the Calculator

Tips: Simply enter any non-negative number to calculate its real sixth root. The calculator will return "Undefined" for negative inputs since they don't have real sixth roots.

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate sixth roots of negative numbers?
A: Not in the real number system. Negative numbers have complex sixth roots, but this calculator only returns real solutions.

Q2: How precise are the results?
A: Results are rounded to 6 decimal places for readability, but the calculation uses full precision internally.

Q3: What's the sixth root of 0?
A: The sixth root of 0 is 0, since \( 0^6 = 0 \).

Q4: How does this relate to square roots and cube roots?
A: A sixth root is equivalent to taking a square root of a cube root, or vice versa: \( \sqrt[6]{x} = \sqrt{\sqrt[3]{x}} = \sqrt[3]{\sqrt{x}} \).

Q5: What are some practical applications of sixth roots?
A: Sixth roots appear in various engineering calculations, physics equations (like inverse sixth power laws), and in some financial models.