Radical (Nth Root) Calculator

Radical Calculator

Radical calculator is used to simplify radical expressions. A radical expression is any mathematical expression containing a square root, cube root, ... up to the nth root. 

What is Radical (Nth Root)?

In mathematics, the radical, specifically the nth root, refers to the operation that calculates the value that, when raised to the power of n, gives a given number. The symbol used to represent the radical is √, known as the radical sign /the square root symbol.

The term "radical" is often used to refer to the square root (√), but it can also represent other roots, such as cube roots (∛), fourth roots (∜), and so on. The number "n" in the nth root indicates the degree of the root. For example, when n = 2, it represents the square root; when n = 3, it represents the cube root, and so on.

To calculate the nth root of a number, you raise that number to the power of 1/n. For instance, if you want to find the cube root of 8, you would solve it as follows:

∛8 = 81/3 = 2

In this case, raising 8 to the power of 1/3 gives you the value of 2, which is the cube root of 8.

How to find the root value?

Example 1:

Determine the fourth root of the number 625.

Solution

It can be expressed in mathematical form

⁴√625

= (5 × 5 × 5 × 5)^1/4

= (5⁴)^1/4

= 5

Example 2:

Determine the Sixth root of the number 64

Solution

In mathematical form, it can be expressed as:

⁶√64

= (64)^1/6

= (2 × 2 × 2 × 2 × 2 × 2)^1/6

= (2⁶)^1/6

= 2

Example 3:

Find the 4^th root of the number 196

Solution

In mathematical form, it can be expressed as:

⁴√196

= (196)^1/4

= (4 × 4 × 4 × 4)^1/4

= (4⁴)^1/4

= 4