To find the cube root of 1000, we can denote it as [tex]\(\sqrt[3]{1000}\)[/tex]. The cube root of a number [tex]\(x\)[/tex] is the number [tex]\(y\)[/tex] such that [tex]\(y^3 = x\)[/tex].
Here's a step-by-step solution:
1. Identify the target value:
- We need to find a number [tex]\(y\)[/tex] such that [tex]\(y^3 = 1000\)[/tex].
2. Understand the properties of cube roots:
- The cube root of a number is the value that, when multiplied by itself twice (i.e., [tex]\(y \times y \times y\)[/tex]), gives the original number.
- For whole numbers, certain cube roots are easy to identify, for instance: [tex]\(\sqrt[3]{1} = 1\)[/tex], [tex]\(\sqrt[3]{8} = 2\)[/tex], and so on.
3. Estimate the value:
- Since [tex]\(1000\)[/tex] is a round number and the cube root of [tex]\(1000\)[/tex] is commonly known, we recall that [tex]\(10 \times 10 \times 10 = 1000\)[/tex]. Hence, a good initial estimate is [tex]\(10\)[/tex].
4. Confirm the calculation:
- Calculating [tex]\(10^3\)[/tex], we get [tex]\(10 \times 10 \times 10 = 1000\)[/tex].
So, the number [tex]\(y\)[/tex] that satisfies [tex]\(y^3 = 1000\)[/tex] is 10.
However, considering significant figures and rounding precision:
The precise cube root of 1000 is actually closer to [tex]\(9.999999999999998\)[/tex] but for most practical purposes, it is taken as:
[tex]\[
\boxed{9.999999999999998}
\][/tex]
