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. It is represented mathematically as \( \sqrt[6]{x} \) or \( x^{\frac{1}{6}} \).

2. How Does the Calculator Work?

The calculator uses the sixth root formula:

Where:

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

Explanation: The calculator raises the input number to the power of 1/6 to find its sixth root.

3. Mathematical Explanation

Details: For real numbers, sixth roots only exist for non-negative numbers. The sixth root function is the inverse of raising a number to the sixth power.

4. Using the Calculator

Tips: Enter any non-negative number to calculate its real sixth root. The result will be undefined for negative numbers in the real number system.

5. Frequently Asked Questions (FAQ)

Q1: Can you take the sixth root of a negative number?
A: Not in the real number system. In complex numbers, negative numbers have sixth roots, but this calculator only returns real roots.

Q2: What's the relationship between sixth roots and cubes?
A: The sixth root of a number is the square root of its cube root, or the cube root of its square root.

Q3: What are some examples of sixth roots?
A: The sixth root of 64 is 2 (since 2×2×2×2×2×2=64). The sixth root of 1 is 1, and the sixth root of 0 is 0.

Q4: How precise are the results?
A: Results are rounded to 6 decimal places for readability, but calculations use full precision.

Q5: Can I calculate sixth roots of very large numbers?
A: Yes, but extremely large numbers may be limited by your computer's floating-point precision.