Root Calculator
Calculate square roots, cube roots, and nth roots with precision
Root Calculator
Calculate square roots, cube roots, and nth roots of any number. The general root, or the nth root of a number a is another number b that when multiplied by itself n times, equals a.
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√ Square Root Calculator
📊 Result
Note: For perfect squares, the result will be exact. For other numbers, the result is calculated to high precision.
∛ Cube Root Calculator
Result
ⁿ√ General Root Calculator
Calculate the nth root of any number. The nth root of a number a is another number b that when multiplied by itself n times equals a.
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📚 Understanding Roots
Square Roots
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √25 = 5 because 5 × 5 = 25.
Cube Roots
The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, ∛27 = 3 because 3 × 3 × 3 = 27.
nth Roots
The nth root of a number is a value that, when raised to the power of n, gives the original number. Generally expressed as ⁿ√a = b where bⁿ = a.
Mathematical Background
In mathematics, the general root, or the nth root of a number a is another number b that when multiplied by itself n times, equals a. In equation format:
Estimating Roots
Some common roots include the square root, where n = 2, and the cubed root, where n = 3. Calculating square roots and nth roots can be done using iterative methods or modern algorithms for high precision results.
For perfect powers (like 4, 9, 16, 25 for square roots), the result will be exact. For other numbers, modern calculators use advanced algorithms to provide highly accurate approximations.