How do you calculate a square root?

A square root of a number n is a value x such that x squared equals n (x x x = n). Our calculator uses efficient numerical algorithms to compute square roots with configurable precision. For example, the square root of 16 is 4, because 4 x 4 = 16.

What is the difference between square root and cube root?

A square root finds a number that multiplied by itself gives the original number (2nd root). A cube root finds a number that multiplied by itself three times gives the original number (3rd root). For example, the square root of 64 is 8, while the cube root of 64 is 4.

Can you calculate the square root of a negative number?

In real number arithmetic, the square root of a negative number is not defined. However, in complex numbers, the square root of a negative number involves the imaginary unit i, where i = sqrt(-1). Our calculator works with real non-negative numbers.

What is an irrational square root?

An irrational square root is a square root that cannot be expressed as a simple fraction and has an infinite, non-repeating decimal expansion. For example, sqrt(2) = 1.41421356... is irrational. Only perfect squares (1, 4, 9, 16, 25, etc.) have rational square roots.

How do I calculate higher-order roots (4th, 5th, etc.)?

Use the optional "Nth Root" field in our calculator. Enter the order of the root you need (e.g., 4 for the 4th root, 5 for the 5th root). The nth root of a number x is calculated as x raised to the power of 1/n. For example, the 4th root of 16 is 2, because 2^4 = 16.

Square Root Calculator

Calculate square roots, cube roots, and nth roots with step-by-step solutions

Enter a Number

Number

Decimal Precision

Optional: Calculate Nth Root

Common Numbers

Square Root Calculation Results

√

Enter a number to calculate

Enter any non-negative number and choose precision

How to Use the Square Root Calculator

Calculate square roots, cube roots, and nth roots with ease

Enter Number

Type any non-negative number into the input field

Set Precision

Choose how many decimal places you want in the result

Optional Nth Root

Enter n to calculate the nth root (e.g., 4 for 4th root)

View Results

See the square root, cube root, verification, and step-by-step process

About Square Root Calculator

What is a Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 x 5 = 25. Square roots are fundamental in mathematics, physics, engineering, and many other fields.

Cube Root

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3, because 3 x 3 x 3 = 27. Cube roots are commonly used in geometry for volume calculations.

Nth Root

The nth root of a number is a value that, when raised to the power of n, gives the original number. This generalizes square roots (n=2) and cube roots (n=3) to any positive integer n.

Precision Control

Our calculator allows you to control the number of decimal places in the result, from 0 to 10 decimal places. This is useful for different applications requiring different levels of accuracy.