Example 1
Completion requirements
| Example 1 |
Simplify the expression \(7\sqrt{2} + 6\sqrt[3]{5} -3\sqrt2 + 4\sqrt[3]{5}\).
Please note that the coefficients are added together, but the radicands remain unchanged.
Add or subtract the coefficients of like radicals.
\(\begin{align}
{\color{blue}7\sqrt 2} {\color{red} + 6\sqrt[3]{5}} {\color{blue}- 3\sqrt 2} {\color{red} + 4\sqrt[3]{5}} &= {\color{blue}\left( {7 - 3} \right)\sqrt 2} {\color{red} + \left( {6 + 4} \right)\sqrt[3]{5}} \\
&= {\color{blue}4\sqrt 2} {\color{red} + 10\sqrt[3]{5}} \\
\end{align}\)
The expression cannot be simplified any further.
\(\begin{align}
{\color{blue}7\sqrt 2} {\color{red} + 6\sqrt[3]{5}} {\color{blue}- 3\sqrt 2} {\color{red} + 4\sqrt[3]{5}} &= {\color{blue}\left( {7 - 3} \right)\sqrt 2} {\color{red} + \left( {6 + 4} \right)\sqrt[3]{5}} \\
&= {\color{blue}4\sqrt 2} {\color{red} + 10\sqrt[3]{5}} \\
\end{align}\)
The expression cannot be simplified any further.
Please note that the coefficients are added together, but the radicands remain unchanged.