Can I take the square root of negative numbers?

In real numbers, you cannot take the square root of negative numbers. However, cube roots and other odd-indexed roots of negative numbers are valid and give negative results.

What's the difference between √16 and ±√16?

√16 refers to the principal (positive) square root, which is 4. ±√16 means both positive and negative square roots: +4 and -4. Most calculators return only the principal root.

How do fractional roots work?

Fractional exponents represent roots: x^(1/2) = √x, x^(1/3) = ∛x, x^(2/3) = (∛x)², etc. The denominator indicates the root, and the numerator indicates the power.

What are perfect squares and perfect cubes?

Perfect squares are numbers whose square roots are integers (4, 9, 16, 25...). Perfect cubes are numbers whose cube roots are integers (8, 27, 64, 125...). These have exact root values.

Root Calculator – Square Root, Cube Root, nth Root

Calculate square roots, cube roots, and nth roots of any number. Supports positive and negative numbers with precise calculations.

Root Calculator – Square Root, Cube Root, nth Root

Calculate square roots, cube roots, and nth roots of any number. Supports positive and negative numbers with precise calculations.

Number*

Number to find the root of

Root Type*

Type of root to calculate

Custom Root Index

Root index for custom roots (e.g., 4 for fourth root)

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Math visualization will appear here

Understanding Roots

A root is the inverse operation of exponentiation. The nth root of a number x is a value that, when raised to the power n, gives x. For example, the square root of 16 is 4 because 4² = 16.

Types of Roots

Common root types:

Square Root (√): Most common, asks "what number squared gives this?"
Cube Root (∛): Asks "what number cubed gives this?"
Fourth Root: Asks "what number to the fourth power gives this?"
nth Root: General form for any positive integer n
Principal Root: The positive root (when multiple roots exist)

How to Use This Calculator

Follow these simple steps to get accurate results:

Enter your number
Enter your root type
Enter your custom root index
Click the "Calculate" button to see your results
Review the detailed breakdown and explanation

Why Use Our Root Calculator – Square Root, Cube Root, nth Root?

100% free and no registration required
Instant, accurate calculations with professional formulas
Mobile-friendly design that works on any device
Privacy-focused - your data never leaves your browser
Educational content to help you understand the results

Frequently Asked Questions

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