Table of Contents
What is Nth Root?
Nth Root is the process of extracting the Nth root of a number. For example, the 3rd root of 8 is 2.
Nth Root Definition
The nth root of a number is the number that you would have to raise to the nth power to get the original number. For example, the fourth root of 64 is 4 because 4 raised to the fourth power is 64.
Nth Root Symbol
The nth root symbol is a mathematical symbol used to denote the nth root of a number. The nth root of a number is the number that, when raised to the power of n, equals the original number. For example, the 3rd root of 64 is 8, because 8 is the number that, when raised to the power of 3, equals 64.
Real Numbers
A real number is a number that exists on the number line. It includes all the rational and irrational numbers.
Rational Numbers
A rational number is any number that can be expressed as a fraction, or a ratio of two integers. In other words, a rational number is a number that can be written in the form p/q, where p and q are both integers.
The set of all rational numbers is denoted by the symbol Q.
Some examples of rational numbers are:
1/2
3/5
-7/8
The number 1/2 can be expressed as the ratio of two integers, 1 and 2. The number 3/5 can be expressed as the ratio of two integers, 3 and 5. The number -7/8 can be expressed as the ratio of two integers, -7 and 8.
All of the numbers above are rational numbers.
Irrational Numbers
An irrational number is a real number that cannot be expressed as a rational number. This means that it cannot be written as a fraction of two integers. Irrational numbers are found in many places in mathematics and physics.
Some of the most famous irrational numbers are π and e.
Complex Numbers
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.
Complex numbers can be used to solve problems in physics and engineering. They are also used in mathematics to solve problems in calculus and other areas of mathematics.
Square Roots
The square root of a number is the number that, when multiplied by itself, results in the original number. For example, the square root of 9 is 3 because 3 multiplied by itself is 9.
Cube Roots
In mathematics, a root is a number that, when multiplied by itself, produces a given number.
For example, the root of 9 is 3 because 3 multiplied by 3 is 9.
The cube root of 64 is 4 because 4 multiplied by 4 multiplied by 4 is 64.
How to find the Nth Root of a Number?
The nth root of a number is the number that you get when you take the nth root of that number. To find the nth root of a number, you first need to know what the nth root of that number is.
When does the Nth Root exist?
The Nth Root exists when the Nth root of a number is a real number.
Properties of Nth Root
The nth root of a number is the number that, when raised to the power of n, equals the original number.
For example, the fourth root of 64 is 4, because 4 raised to the power of 4 equals 64.
The nth root of a number can also be found using a calculator or a computer algebra system.
Simplifying Nth Root
Nth root is the inverse operation of taking the nth root of a number.
To simplify an nth root, divide the number by the root.
