Example 3
Completion requirements
| Example 3 |
Multimedia |
Simplify \(\frac{3}{{\sqrt[3]{2}}}\).
This time, in order to remove the cube root from the denominator, you must change the radicand so that it has an exponent of three. Therefore, multiply both numerator and denominator by \(\left( {\sqrt[3]{2}} \right)^2 \).
Recall that \(\sqrt[n]{{x^n }} = x\), hence why the numerator and denominator are multiplied by the radical squared.
\(\begin{align}
\frac{3}{{\sqrt[3]{2}}} &= \frac{3}{{\sqrt[3]{2}}}\cdot \frac{{\left( {\sqrt[3]{2}} \right)^2 }}{{\left( {\sqrt[3]{2}} \right)^2 }} \\
&= \frac{{3\left( {\sqrt[3]{2}} \right)^2 }}{{\sqrt[3]{{2^3 }}}} \\
&= \frac{{3\sqrt[3]{4}}}{2} \\
\end{align}\)
\frac{3}{{\sqrt[3]{2}}} &= \frac{3}{{\sqrt[3]{2}}}\cdot \frac{{\left( {\sqrt[3]{2}} \right)^2 }}{{\left( {\sqrt[3]{2}} \right)^2 }} \\
&= \frac{{3\left( {\sqrt[3]{2}} \right)^2 }}{{\sqrt[3]{{2^3 }}}} \\
&= \frac{{3\sqrt[3]{4}}}{2} \\
\end{align}\)
Recall that \(\sqrt[n]{{x^n }} = x\), hence why the numerator and denominator are multiplied by the radical squared.