Root Calculation

1. Enter the "value (x)" for which you want to find the square root.
2. If it is not the square root, enter the "power root (n)".
3. The "value resulting from the root calculation" will be calculated automatically.

Square Root

A square root is a number that, when you square a number, returns to the original number. The square root is represented by the symbol "√".

Example: √9 = 3 (3 squared is 9, so the square root of 9 is 3)

nth Root

nth root is the number that you multiply a number by n times to get the original number. When n is 3, it is also called a "cube root", and when n is 2, it is a square root.

Example: ³√27 = 3 (3 multiplied three times is 27, so the cube root of 27 is 3)

Radical Sign

The symbol "√" is called the "radical sign" and is used to calculate square roots and nth roots. When it is an nth root, "n" is written in the upper left corner of the root.

Example: ³√8 (cube root of 8)

Complex roots

The square root of a negative number does not exist for real numbers, but it is defined for complex numbers.

Example: √-1 = i (imaginary unit)

How to calculate square roots

The square root is the number that is obtained by squaring a number to return to the original number. The formula for finding the square root is as follows:

√x = y (where "y" is a number that satisfies "y² = x")

Example: √9 = 3 (where "3" is a number that satisfies "3² = 9")

How to calculate n-th roots

An n-th root is a number that, when multiplied n times, gives the original number.

[n]√x = y (where "y" is a number that satisfies "yⁿ = x")

3√27 = 3 (where "3" is a number that satisfies "3³ = 27")

4√16 = 2 (where "2" is a number that satisfies "2⁴ = 16")

How to calculate by hand

It can be difficult to calculate the square root by hand, so the following methods are used.

• Approximation method (Babylonian method or Newton method)A method of iteratively finding an approximate value. For example, a set initial value is determined and the approximation of the square root is repeated.
• Prime factorizationSometimes it is easier to calculate the square root by decomposing a number into prime factors.
• Calculators and calculation toolsYou can instantly calculate the square root by pressing the square root button on a calculator.

This tool is available for free.