Free Fourth Root Calculator | Unit Converters
Fourth Root Calculator
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What is Fourth Root?
Fourth root is like asking "what number, when multiplied by itself 4 times, gives me this number?" It's the opposite of raising a number to the 4th power.
Think of it like this: if 2 × 2 × 2 × 2 = 16, then the fourth root of 16 is 2. We write this as ⁴√16 = 2.
Fourth roots are useful in math, science, and engineering when you need to find the original number from its fourth power.
How to Use This Calculator
Type any positive number in the input box. Fourth roots work best with positive numbers.
The calculator will instantly show you the fourth root of that number.
Try different numbers to see the pattern and understand how fourth roots work!
Easy Examples to Understand
Example 1: Perfect Fourth Root
Question: What is ⁴√16?
Step 1: We need to find what number times itself 4 times equals 16
Step 2: Let's try 2: 2 × 2 × 2 × 2 = 16 ✓
Answer: ⁴√16 = 2
Example 2: Another Perfect Fourth Root
Question: What is ⁴√81?
Step 1: We need to find what number times itself 4 times equals 81
Step 2: Let's try 3: 3 × 3 × 3 × 3 = 81 ✓
Answer: ⁴√81 = 3
Example 3: Decimal Answer
Question: What is ⁴√50?
Step 1: 50 is not a perfect fourth power, so we'll get a decimal
Step 2: We know 2⁴ = 16 and 3⁴ = 81, so the answer is between 2 and 3
Answer: ⁴√50 ≈ 2.66 (approximately)
Perfect Fourth Powers You Should Know
These are numbers that have nice, whole number fourth roots:
Perfect Fourth Powers
- 1⁴ = 1, so ⁴√1 = 1
- 2⁴ = 16, so ⁴√16 = 2
- 3⁴ = 81, so ⁴√81 = 3
- 4⁴ = 256, so ⁴√256 = 4
- 5⁴ = 625, so ⁴√625 = 5
- 6⁴ = 1,296, so ⁴√1296 = 6
- 10⁴ = 10,000, so ⁴√10000 = 10
Why Do Fourth Roots Matter?
Fourth roots show up in several important areas:
- Math Problems: Solving equations where x⁴ = some number
- Physics: Some wave and energy calculations use fourth powers
- Engineering: Stress and material calculations
- Computer Graphics: 3D modeling and animations
- Statistics: Some advanced probability calculations
- Finance: Compound interest over multiple periods
Common Questions People Ask
What's the difference between fourth root and square root?
Square root asks "what times itself equals this?" Fourth root asks "what times itself 4 times equals this?" Square root of 16 is 4, but fourth root of 16 is 2.
Can I take fourth roots of negative numbers?
In basic math, we usually only work with fourth roots of positive numbers. Negative numbers make it more complicated because you get complex numbers.
How is fourth root related to square root?
Fourth root is actually the square root of the square root! So ⁴√x = √(√x). This makes it easier to calculate sometimes.
Why do most fourth roots give decimal answers?
Most numbers aren't perfect fourth powers. Just like most numbers don't have nice square roots, most fourth roots are decimals too.
How can I check if my fourth root is correct?
Take your answer and multiply it by itself 4 times. If you get back to your original number (or very close), then it's correct!
Tips for Success
✓ Memorize Perfect Fourth Powers
Learn 1⁴=1, 2⁴=16, 3⁴=81, 4⁴=256, 5⁴=625 by heart.
✓ Use the Square Root Trick
Remember that ⁴√x = √(√x). Find the square root twice!
✓ Check Your Work
Always verify by raising your answer to the 4th power to see if you get back the original number.
✓ Use Estimation
If your number is between two perfect fourth powers, your answer is between their fourth roots.