Question

Find the solution for x when x^3=27/8.

Answer 1

To solve the equation \( x^3 = \frac{27}{8} \), we follow these steps:

1. Take the cube root of both sides of the equation:

\[
x = \sqrt[3]{\frac{27}{8}}
\]

2. We can separate the cube root into the numerator and denominator:

\[
x = \frac{\sqrt[3]{27}}{\sqrt[3]{8}}
\]

3. Now calculate the cube roots:

\[
\sqrt[3]{27} = 3 \quad \text{and} \quad \sqrt[3]{8} = 2
\]

Thus,

\[
x = \frac{3}{2}
\]

So the solution for \( x \) is:

\[
\boxed{\frac{3}{2}}
\]