Select the correct answer.
What is this expression in simplified form?
[tex]$\sqrt[3]{1,000}$[/tex]
A. 333
B. 100
C. 31
D. 10
Answer (2)
The problem asks to simplify the cube root of 1000, which is 3 1000 .
We need to find a number x such that x 3 = 1000 .
Since 10 × 10 × 10 = 1000 , we have 1 0 3 = 1000 .
Therefore, the simplified form of 3 1000 is 10 .
Explanation
Understanding the problem We are asked to simplify the cube root of 1000, which is written as 3 1000 . This means we need to find a number that, when multiplied by itself three times, equals 1000.
Finding the cube root We need to find a number x such that x 3 = 1000 . Let's consider some possible values for x . We know that 1 0 3 = 10 × 10 × 10 = 1000 .
Determining the answer Therefore, the cube root of 1000 is 10, which means 3 1000 = 10 .
Examples
Imagine you're organizing boxes in a warehouse, and you want to arrange 1000 identical cube-shaped boxes into a single, larger cube. To find out how many boxes you need along each edge of the larger cube, you would calculate the cube root of 1000. In this case, 3 1000 = 10 , meaning you would need 10 boxes along each edge to form the larger cube. This concept is useful in logistics, packaging, and spatial arrangement problems.
The cube root of 1000, denoted as 3 1000 , simplifies to 10 since 1 0 3 = 1000 . Thus, the correct answer is option D. 10.
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