The formula to calculate the Fourth Root is:
\[ \text{Fourth Root} = X^{\frac{1}{4}} \]
Where:
Let's say the number (X) is 16. Using the formula:
\[ \text{Fourth Root} = 16^{\frac{1}{4}} \]
We get:
\[ \text{Fourth Root} \approx 2.00 \]
So, the fourth root of 16 is approximately 2.00.
Definition: The fourth root of a number is a value that, when multiplied by itself four times, gives the original number.
Formula: \( \sqrt[4]{x} = x^{\frac{1}{4}} \)
Example: \( \sqrt[4]{16} = 16^{\frac{1}{4}} \)
Definition: The complex fourth roots of a number include all possible values that, when raised to the fourth power, yield the original number.
Formula: \( \sqrt[4]{z} = \sqrt[4]{r} \left( \cos \frac{\theta + 2k\pi}{4} + i \sin \frac{\theta + 2k\pi}{4} \right) \)
Example: \( \sqrt[4]{1} = 1 \left( \cos \frac{0 + 2k\pi}{4} + i \sin \frac{0 + 2k\pi}{4} \right) \)
