Final answer:
The given mathematical expression 1 - 1/ ³√(1 - 1/√3) simplifies to a final answer of -0.33 after a series of steps which includes finding the square root and cube root.
Step-by-step explanation:
The subject of this question is Mathematics and it's a High School-level problem. The question requires understanding of cube roots and square roots and their manipulation.
Now, let's start to simplify the expression 1 - 1/ ³√(1 - 1/√3) step-by-step. First, we should solve the expression at the deepest bracket level, which is 1/√3. Here, √3 ~ 1.732 so, 1/1.732 is approximately equal to 0.577.
Substituting this value back into the expression, we have, 1 - 1/ ³√(1 - 0.577) which becomes 1 - 1/ ³√(0.423). The cube root of 0.423 is ~0.753. So the expression further simplifies to become 1 - 1/0.753.
Eventually, the final expression becomes 1- 1.33. This results in a negative number: -0.33, which is the direct answer in two lines.
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