Let's solve the problem step-by-step:
We are asked to find the cube root of [tex]\(\frac{2}{3}\)[/tex], denoted as [tex]\(\sqrt[3]{\frac{2}{3}}\)[/tex].
1. Identify the given fraction:
The fraction we need to consider is [tex]\(\frac{2}{3}\)[/tex].
2. Understand the operation:
We need to find the cube root of this fraction. The cube root of a number [tex]\(x\)[/tex] is a number [tex]\(y\)[/tex] such that [tex]\(y^3 = x\)[/tex].
3. Apply the operation:
For [tex]\(\frac{2}{3}\)[/tex], we need to determine the value of [tex]\(y\)[/tex] such that:
[tex]\[
y^3 = \frac{2}{3}
\][/tex]
4. Determine the cube root:
When calculating this operation, we find that the cube root of [tex]\(\frac{2}{3}\)[/tex] is approximately:
[tex]\[
\sqrt[3]{\frac{2}{3}} \approx 0.8735804647362988
\][/tex]
5. Conclusion:
Therefore, the cube root of [tex]\(\frac{2}{3}\)[/tex] is approximately [tex]\(0.8735804647362988\)[/tex].
