What is the nth Root of a Number?
Contents
The ‘nth root’ of a number is a number that multiplied by itself ‘n’ times to get the initial value.
nth roots are represented by the symbol n√. To find the nth root of a number we have to find that number, whose ‘n’ times multiplication by itself gives the number for which we have to find the nth root.
Therefore the number that multiplied by itself n times is the nth root of the given number.
Here n can be any number 2, 3, 4, 5 …… etc.
nth Root Exponents in Algebra Explained
For example, Find the nth root of ‘a’ or can say find n√a
It is just (1/n)th root of the number same as square root then it is 1/2 the root and the cube root then it is 1/3 root. Therefore, nth root can be represented as 1/n exponentially.
In exponents, we can represent it as n√a = a1/n
2nd root is square root √y x √y = y1/2 x y1/2 = y
3rd root is cube root ∛y x ∛y x ∛y = y1/3 x y1/3 x y1/3 = y
nth root is nth root. n√y x n√y x n√y x…… n√y (n times) = y
Rather than using 4th, 5th, etc. generally, we can use nth.
Using nth root is a general way of writing roots it can be 2nd root (square root), 3rd root (cube root), 4th root, 5th root etc.
| Root Examples | Root Name | Equation |
|---|---|---|
| 2nd root | Square Root | √y x √y = y1/2 x y1/2 = y |
| 3rd root | Cubed Root | ∛y x ∛y x ∛y = y1/3 x y1/3 x y1/3 = y |
| nth root | nth Root | n√y x n√y x n√y x…… n√y (n times) = y |
nth Root Example
How to Find the nth root of a number
Example: Find ‘n’ in this question.
n√32 = 2
Solution: The value of n√32 is 2. So, we have to factorize 32 in terms of 2.
32 = 2 ×2 × 2 ×2×2
n√32 = 2
n√2 ×2 × 2 ×2×2 = 2
2 is multiplied here 5 times to get 32.
Therefore, the value of n is 5.
nth Root Properties
How to multiple and divide nth root functions.
Multiplication and Division properties
How to add and subtract nth root functions.
Addition and Subtraction properties
The Link between Roots and Exponents Root on one side of the equals to ‘=’ can be changed to exponents on the other side of the equals to ’=’.
If = n√y then x = yn.
For example: n√81 = 3
so, 81 = 34.
nth Root of Unity
The nth root of a unity is a complex number that equals 1 when it is raised to the power of a positive integer. The nth root of a unity has common applications in geometry, number theory, and other areas of mathematics.
nth Root Excel
Calculating the nth root in excel is simple with the power of function. Unfortunately, excel does not have let you use the square root SQRT function for nth roots.
To calculate the nth root formula in excel simply raise your to the power of 1/n.
For example, if I wanted to find the 12th root of 10, I would use this nth root formula in excel
=10^(1/12)