## Roots - how to calculate the square root of a number? The most important patterns

The elements keep many students awake at night. Is square root really difficult? Not necessarily, as long as we remember one rule: to find the square root of a given number, we need to find a number that, when raised to the second power, gives the number under the square. Sounds complicated? Let's see how it works with examples.

## 1. Square root - what is it?

Rooting is the opposite of exponentiation. To understand what the elements are, how they are written, and how to calculate them, we'll start by explaining what each symbol means and discussing the most important formulas.

The basic formula for the elements is:

The formula for calculating the square root

We can read the above entry:

The nth root of a is b when b to the nth power is a ".

In this record:

n - is the degree of the element,

a - sub-elemental number,

b - the nth root of the number a, the result of the square root.

We can also determine the roots for complex numbers.

In higher mathematics, the complex roots of ones play a very important role.

The roots of ones are also called de Moivre numbers to honor the French mathematician Abraham de Moivre.

The nth degree roots of unity are on the complex plane the vertices of a regular polygon with n sides that are inscribed in the unit cycle. Its one vertex lies at point 1.

Roots of n degree z 1 on the complex plane (Wikipedia)

The vertices divide the circle into n equal parts.

## 2. Elements - important formulas

Calculating the square root of a number is just the beginning. Below, let us analyze other significant formulas related to the square root.

Root formula:

Root formula

It follows from the following that a is a number greater than or equal to 0. In turn, n and m are natural numbers (except the numbers 0 and 1).

The formula for the sum of the elements:

The formula for the sum of the elements

The notation means that the numbers a and b are greater than or equal to 0.

The formula for multiplying the roots:

The formula for multiplying the roots

A and b are numbers that are greater than or equal to 0. And n and m are natural numbers excluding the numbers 0 and 1.

The formula for dividing elements:

The formula for dividing elements

In the above notation: a is a number greater than or equal to 0.

B is a number greater than 0.

N and m are natural numbers excluding the numbers 0 and 1.

The formula for the power of an element:

The formula for the power of an element

Where a is a number greater than or equal to 0.

N and m are natural numbers excluding the numbers 0 and 1.

Formula for the absolute value of the elements:

The formula for the absolute value of elements

This means that the numbers a and b are greater than or equal to 0.