Square Root Calculator
Free square root calculator. Calculate the square root, cube root, or any nth root of a number with exact and decimal results. Includes perfect square detection and simplification of radical expressions.
What Is a Root in Mathematics?
A root is the inverse operation of exponentiation. The nth root of a number is the value that, raised to the power n, produces that number. For example, the square root of 9 is 3, because 3² = 9.
Types of Roots
Square root: index 2, the most common type. Cube root: index 3, often used in volume calculations. Nth root: any index greater than 1, useful in advanced math and engineering.
Frequently Asked Questions
Can you take the square root of a negative number?
Not in the real number system. An even root of a negative number is not defined for real numbers, but odd roots of negative numbers are valid (for example, the cube root of -8 is -2).
What are the properties of roots?
Key properties include: the root of a product equals the product of the roots, and the root of a quotient equals the quotient of the roots. These make simplification easier.