1. What is Fourth Root?

The fourth root of a number is a value that, when multiplied by itself three times (raised to the fourth power), equals the original number. Mathematically, if \( y = \sqrt[4]{x} \), then \( y^4 = x \).

2. How Does the Calculator Work?

The calculator uses the following mathematical formula:

This can also be calculated as:

Where:

• \( x \) — The number you want to find the fourth root of (must be ≥ 0)
• \( \sqrt[4]{x} \) — The fourth root of x

3. Applications of Fourth Root

Details: Fourth roots are used in various fields including physics (wave equations), engineering (stress calculations), and finance (compound interest models).

4. Using the Calculator

Tips: Enter any non-negative number to calculate its fourth root. The result will be displayed with 4 decimal places.

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate fourth roots of negative numbers?
A: In real numbers, no. Negative numbers don't have real fourth roots. In complex numbers, they do have fourth roots.

Q2: How is fourth root different from square root?
A: Square root is the second root (\( \sqrt{x} \)), while fourth root is the fourth root (\( \sqrt[4]{x} \)). The fourth root is the square root of the square root.

Q3: What's the fourth root of common numbers?
A: Examples: \( \sqrt[4]{16} = 2 \), \( \sqrt[4]{81} = 3 \), \( \sqrt[4]{256} = 4 \).

Q4: How can I calculate fourth roots without a calculator?
A: You can use logarithms or iterative approximation methods, but a calculator is much easier.

Q5: Are there practical uses for fourth roots?
A: Yes, in physics (wave equations), engineering (stress analysis), and statistics (data transformations).