Nth Root Calculator
Calculate any root of a number.
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Table of Contents
Root Concept
The nth root of a number is a value that, when multiplied by itself n times, gives the original number. Common types of roots include:
- Square Root (n=2): The value that, when multiplied by itself, gives the original number.
- Cube Root (n=3): The value that, when multiplied by itself three times, gives the original number.
- Higher Order Roots: Any root where n > 3.
Calculation Methods
Here are the steps to calculate an nth root:
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1Identify the number (x) and the root order (n)
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2Check if the calculation is valid (e.g., no even root of negative numbers)
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3Apply the formula: x^(1/n)
For example, to calculate the cube root of 27:
27^(1/3) = 3
Because 3 × 3 × 3 = 27
Root - Practical Examples
Example 1 Square Root
Calculating the square root of a number.
Number: 16
Root order: 2
Result: 4 (because 4 × 4 = 16)
Example 2 Cube Root
Calculating the cube root of a number.
Number: 125
Root order: 3
Result: 5 (because 5 × 5 × 5 = 125)
Example 3 Fourth Root
Calculating the fourth root of a number.
Number: 81
Root order: 4
Result: 3 (because 3 × 3 × 3 × 3 = 81)