To solve the equation [tex]\(u^3 = 23\)[/tex] where [tex]\(u\)[/tex] is a real number, we need to isolate [tex]\(u\)[/tex].
We start by recognizing that if [tex]\(u\)[/tex] is a real number such that [tex]\(u^3 = 23\)[/tex], then [tex]\(u\)[/tex] must be the cube root of 23. The cube root can be denoted as [tex]\( \sqrt[3]{23}\)[/tex].
Therefore, to solve for [tex]\(u\)[/tex], we take the cube root of both sides of the equation:
[tex]\[ u = \sqrt[3]{23} \][/tex]
By evaluating [tex]\(\sqrt[3]{23}\)[/tex], we find that:
[tex]\[
u \approx 2.8438669798515654
\][/tex]
So, the real number [tex]\(u\)[/tex] that satisfies the equation [tex]\(u^3 = 23\)[/tex] is approximately [tex]\(u = 2.8438669798515654\)[/tex].
To simplify the expression to its most concise mathematical form:
[tex]\[ u = \sqrt[3]{23} \][/tex]
