how is the sixth root of 356 related to the eleventh root of 356?
To understand the relationship between the sixth root of 356 and the eleventh root of 356, we need to know how to calculate these roots.
The nth root of a number x is calculated by raising x to the power of 1/n.
If we apply this formula, we can find the sixth root and the eleventh root of 356:
1. For the sixth root of 356:
- Calculate 356 raised to the power of 1/6:
- (356)^(1/6) ≈ 4.240253
2. For the eleventh root of 356:
- Calculate 356 raised to the power of 1/11:
- (356)^(1/11) ≈ 2.500415
So, the sixth root of 356 is approximately 4.240253, and the eleventh root of 356 is approximately 2.500415.
Now, to understand their relationship, we can compare the values:
- The sixth root of 356 is larger than the eleventh root of 356. This means that the number 4.240253 is greater than 2.500415.
In general, when comparing roots of the same number, the larger the root, the smaller the resulting value. So, the eleventh root of 356 is smaller than the sixth root of 356.