第四根计算器

一般来说，一个数的 n^次根是一个数与自身相乘 n 次。一个数的 4^次方根是 n^次方根数，其中 n = 4，即一个数与自身相乘 4 次。数 x 的 n^次根表示为ⁿ √x。

数字的 4^次方根

The 4^th Root of a number is a number when multiplied four times by itself, then the result obtained will be the original number. We can also call it a double square root because 4^th root of a number is the square root of a number. Let’s move into an exam to get more understanding.

Any number which is having the power of 4 can be taken out of the 4th root. For example, a⁴ is a number in the 4^th root and we can take it out from the 4^th root as a. i.e., ⁴√a⁴=a. 

In the above sample example, 4^th root and power 4 get canceled to each other.

示例问题

问题 1：求 16 的 4^次方根

解决方案：

When 2 is multiplied 4 times by itself we get 16.

i.e., 2⁴ = 2 × 2 × 2 × 2 = 16

So 2 is the 4^th root of 16.

问题2：求⁴ √256

解决方案：

⁴√256 = ⁴√(4 × 4 × 4 × 4)

= 4

So 4th root of 256 is 4

问题 3：求 81 的 4^次根

解决方案：

When 3 is multiplied 4 times by itself we get 81.

i.e., 3⁴ = 3 × 3 × 3 × 3 = 81

So 3 is 4^th root of 81.

问题4：找到⁴ √4096？

解决方案：

⁴√4096 = ⁴√(8 × 8 × 8 × 8)

= 8

So 4^th root of 4096 is 8

问题 5：求 48 的 4^次方根

解决方案：

48 can be written as 2 × 2 × 2 × 2 × 3

⁴√48 = ⁴√(2 × 2 × 2 × 2 × 3)

= ⁴√(2⁴ × 3)

= 2 × ⁴√3

So, ⁴√48 = 2 × ⁴√3

In this problem 2 to the power of 4 is taken out from the 4^th root as 2. Like this, we can take any number with power as 4 from the 4^th root.

问题 6：找到数字 32 的 4^次根？

解决方案：

⁴√32 = ⁴√(2 × 2 × 2 × 2 × 2)

= ⁴√(2⁴ × 2)

= 2 × ⁴√2

So, ⁴√32 = 2 × ⁴√2

问题 7： ⁴ √96 的结果是什么。

解决方案：

⁴√96 = ⁴√(2 × 2 × 2 × 2 × 2 × 3)

= ⁴√(2⁵ × 3)

= ⁴√(2⁴ × 2 × 3)

= 2 × ⁴√(2 × 3)

= 2 × ⁴√6

Hence 4^th root of 96 is 2 × ⁴√6