Example 1
Completion requirements
| Example 1 |
Simplify the expression \(2\sqrt 5 \cdot 4\sqrt 6 \).
Step 1: Multiply the coefficients together and multiply the radicands together.
\(\begin{align}
2\sqrt 5 \cdot 4\sqrt 6 &= \left( {2\cdot 4} \right)\sqrt {5\cdot 6} \\
&= 8\sqrt {30} \\
\end{align}\)
Step 2: Check to see if the radical can be simplified any further.
In this example, there are no perfect square factors of \(30\), therefore the radical is simplified.
\(2\sqrt 5 \cdot 4\sqrt 6 = 8\sqrt {30} \)
\(\begin{align}
2\sqrt 5 \cdot 4\sqrt 6 &= \left( {2\cdot 4} \right)\sqrt {5\cdot 6} \\
&= 8\sqrt {30} \\
\end{align}\)
Step 2: Check to see if the radical can be simplified any further.
In this example, there are no perfect square factors of \(30\), therefore the radical is simplified.
\(2\sqrt 5 \cdot 4\sqrt 6 = 8\sqrt {30} \)