第n个根

实数是包括有理数和无理数的数。有理数，例如整数(-2、0、1)，分数(1 / 2、2.5)和无理数，例如√3，π(22/7)等，都是实数。实数的第n个根的定义可以表示为：

For any two real numbers a and b, and any positive integer n, if aⁿ = b, then a is an nth root of b. 

例如：

3⁴ = 81

Where,

a = 3, b = 81, and n = 4

That means that 3 is the fourth root of 81.

如何写第n个根?

$\sqrt[n]{}$ indicates an nth root. 

例如：

$\sqrt[n]{144}$

Where,

144 = Radicand,

√ = Radical Sign, and

n = Index

That means that we are taking the nth root of 144. One can take any value of n, like n = 2, 3, 5, etc. We will be taking that root of 100.

主根

一些数字的根数不止一个。例如，36有两个根，一个是+6，另一个是-6。在这种情况下，非负根称为主体根。

如果未指定索引，则根号表示主根。例如，如果我们采取$\sqrt{36}$那么我们在说它的主根是6

例子

例1：如果n = 5且b = 32，则a =?

解决方案：

Given: a⁵ = 32

=> $a=\sqrt[5]{32}$

2 . 2 . 2 . 2 . 2 = 32 

Since, 2 is the fifth root of 32

Therefore, a = 2

示例2：n = 6，b = 4096，然后a =?

解决方案：

Given: a⁶ = 4096

=> $a=\sqrt[6]{4096}$

To find the value of a, we will check which integer value is the sixth root of 4096

2 . 2 . 2 . 2 . 2 . 2 = 64 

3 . 3 . 3 . 3 . 3 . 3 = 729 

4 . 4 . 4 . 4 . 4 . 4 = 4096 

Since, 4 is the sixth root of 4096 

Therefore, a = 4

示例3：如果a = 18，b = 2，n = 2，并且$c= ( \sqrt[n]{a}\ * \sqrt[n]{b})$然后找到c的值?

解决方案：

Given: $c = ( \sqrt[n]{a}\ * \sqrt[n]{b})$

SInce the index value is same then the radicand is multiplied

$\\ c=( \sqrt[2]{18} * \sqrt[2]{2})\\ c= \sqrt[2]{36}$

Since, 6 is the square root of 36 (6² = 36) 

Therefore, c = 6

示例4：如果a = 5，b = 15，n = 3并且$c = ( \frac{\sqrt[n]{a}}{\sqrt[n]{b}})$然后找到c的值?

解决方案：

Given: $c = ( \frac{\sqrt[n]{a}}{\sqrt[n]{b}})$

SInce the index value is same then the radicand are divided

$\\ c = \sqrt[n]{\frac{a}{b}} \\ c = \sqrt[3]{\frac{5}{15}}\\ c = \sqrt[3]{\frac{1}{3}}\\ c = \frac{1}{\sqrt[3]{3}}$

示例5：解决以下问题： $c = \sqrt[3]{1} +\sqrt[3]{ 8}+\sqrt[3]{27}+\sqrt[3]{64}$

解决方案：

Given: $c = \sqrt[3]{1} +\sqrt[3]{ 8}+\sqrt[3]{27}+\sqrt[3]{64}\\ c= \sqrt[3]{1^3} +\sqrt[3]{2^3}+\sqrt[3]{3^3}+\sqrt[3]{4^3}$

1 . 1 . 1 = 1, 1 is the cube root of 1

2 . 2 . 2 = 8, 2 is the cube root of 8

3 . 3 . 3 = 27, 3 is the cube root of 27

4 . 4 . 4 = 64, 4 is the cube root of 64

c = 1 + 2 + 3 + 4 

c = 10