Free Radicals Root Calculator | Unit Converters
Result
2
Expression
ⁿ√8
Index
3
How It Works
Enter Number
Input the number and root index
Calculate Root
Get the nth root instantly
Common Examples You Can Try
Here are everyday situations where radicals and roots help you solve real problems. These examples show how useful root calculations can be in your daily life.
Square Garden Area
Area: 64 sq ft, Find side length
√64 = 8 ft
Find the side length of a square garden when you know the area.
Cube Volume
Volume: 27 cubic units
³√27 = 3 units
Find the side length of a cube when you know its volume.
Investment Growth
$1000 becomes $1331 in 3 years
³√1.331 = 1.1 (10% growth)
Calculate annual growth rate from total return.
Physics Problems
Distance fallen: 16 ft in time t
√(16/16) = 1 second
Calculate time from distance in free fall problems.
Engineering Design
Pipe cross-section area: 78.54 sq in
√(78.54/π) = 5 in radius
Find pipe radius from cross-sectional area.
Population Growth
Population doubles every n years
ⁿ√2 = growth factor
Calculate annual growth rate from doubling time.
Formula & Calculation
Nth Root Formula
ⁿ√x = x^(1/n)
Where n is the root index and x is the radicand (number under the radical)
Common Root Types
- • Square root (n=2): √x
- • Cube root (n=3): ³√x
- • Fourth root (n=4): ⁴√x
- • Fifth root (n=5): ⁵√x
Example Calculation
Find: ³√8
Formula: 8^(1/3)
Calculation: 8^(1/3) = 2
Verification: 2³ = 8 ✓
What are Radicals and Roots?
Radicals and roots are mathematical operations that help you find what number, when multiplied by itself a certain number of times, gives you the original number. The radical symbol (√) shows this operation clearly.
When you see ³√8, it asks: "What number times itself three times equals 8?" The answer is 2, because 2 × 2 × 2 = 8. This makes radicals very useful for solving real-world problems.
Root calculations appear everywhere in daily life. From finding the side of a square garden to calculating growth rates, roots help you work backwards from a final result to find the original value.
Easy to Understand
Radicals are just the opposite of powers. If 2³ = 8, then ³√8 = 2. Simple and logical mathematical relationship.
Practical Uses
Perfect for geometry, physics, engineering, finance, and any situation where you need to find original values from results.
Quick Results
Our calculator gives you instant, accurate results for any root calculation. No complex math needed on your part.
Common Root Calculations Table
| Expression | Result | Verification | Common Use |
|---|---|---|---|
| √16 | 4 | 4² = 16 | Square areas |
| ³√27 | 3 | 3³ = 27 | Cube volumes |
| ⁴√81 | 3 | 3⁴ = 81 | Growth calculations |
| ⁵√32 | 2 | 2⁵ = 32 | Population studies |
| √100 | 10 | 10² = 100 | Measurements |
| ³√125 | 5 | 5³ = 125 | Engineering |
Frequently Asked Questions
What is an nth root in simple terms?
An nth root is a number that when multiplied by itself n times gives you the original number. For example, the 3rd root of 8 is 2, because 2 × 2 × 2 = 8.
How do I know which root to use?
The root index depends on your problem. Use square root (n=2) for areas, cube root (n=3) for volumes, and higher roots for compound growth or complex calculations.
Can I find roots of negative numbers?
Yes, but only for odd roots (3rd, 5th, 7th, etc.). Even roots of negative numbers result in complex numbers, which this calculator doesn't display.
What's the difference between √ and ³√?
√ (square root) finds what number times itself equals the given number. ³√ (cube root) finds what number times itself three times equals the given number.
Are the calculator results accurate?
Yes, this calculator uses precise mathematical formulas. For exact results, it shows whole numbers. For approximate results, it displays up to 6 decimal places for accuracy.