Solved on Dec 24, 2023
What is the number of real fifth roots of 0?
STEP 1
Assumptions
1. We are looking for the number of real fifth roots of 0.
2. A real fifth root of a number is a real number such that .
STEP 2
Understand the definition of a fifth root.
A fifth root of a number is a number such that when is raised to the power of 5, the result is . This can be written as:
STEP 3
Apply the definition to the number 0.
We want to find a real number such that:
STEP 4
Consider the properties of real numbers and multiplication.
For any real number , the only way can equal 0 is if itself is 0. This is because 0 multiplied by any number is 0, and any non-zero number raised to any power is non-zero.
STEP 5
Conclude that 0 is the only real fifth root of 0.
Since no other real number except for 0 raised to the fifth power will result in 0, we can conclude that 0 has exactly one real fifth root, which is 0 itself.
Therefore, the number of real fifth roots that 0 has is 1.
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