Sure, let's find the cube root of the fraction [tex]\(\frac{500}{648}\)[/tex].
1. Simplify the Fraction: First, we simplify the fraction [tex]\(\frac{500}{648}\)[/tex]. However, since we are interested in a detailed process, let's express it as a decimal fraction directly.
[tex]\[
\frac{500}{648} = 0.7716049382716049
\][/tex]
2. Calculate the Cube Root: Next, we calculate the cube root of [tex]\(0.7716049382716049\)[/tex]. The cube root of a number [tex]\(x\)[/tex] is a value [tex]\(y\)[/tex] such that [tex]\(y^3 = x\)[/tex].
[tex]\[
\sqrt[3]{0.7716049382716049} = 0.9172020135818407
\][/tex]
So, the fraction [tex]\(\frac{500}{648}\)[/tex] simplifies approximately to [tex]\(0.7716049382716049\)[/tex], and its cube root is approximately [tex]\(0.9172020135818407\)[/tex].
