Example 1
Completion requirements
| Example 1 |
Simplify the expression \(3\sqrt 7 \left( {5\sqrt 2 - 2} \right)\).
Step 1: Use the distributive property to multiply the monomial by each term in the binomial.
\(\begin{align}
3\sqrt 7 \left( {5\sqrt 2 - 2} \right) &= \left( {3\sqrt 7 \cdot 5\sqrt 2 } \right) + \left( {3\sqrt 7 \cdot \left( {-2} \right)} \right) \\
&= \left[ {\left( {3 \cdot 5} \right)\sqrt {7 \cdot 2} } \right] + \left[ {\left( {3 \cdot \left( {-2} \right)} \right)\sqrt 7 } \right] \\
&= 15\sqrt {14} + \left( {-6} \right)\sqrt 7 \\
&= 15\sqrt {14} - 6\sqrt 7 \\
\end{align}\)
Step 2: Check if any radicals can be further reduced.
Neither radical can be simplified further.
\(3\sqrt 7 \left( {5\sqrt 2 - 2} \right) = 15\sqrt {14} - 6\sqrt 7 \)
\(\begin{align}
3\sqrt 7 \left( {5\sqrt 2 - 2} \right) &= \left( {3\sqrt 7 \cdot 5\sqrt 2 } \right) + \left( {3\sqrt 7 \cdot \left( {-2} \right)} \right) \\
&= \left[ {\left( {3 \cdot 5} \right)\sqrt {7 \cdot 2} } \right] + \left[ {\left( {3 \cdot \left( {-2} \right)} \right)\sqrt 7 } \right] \\
&= 15\sqrt {14} + \left( {-6} \right)\sqrt 7 \\
&= 15\sqrt {14} - 6\sqrt 7 \\
\end{align}\)
Step 2: Check if any radicals can be further reduced.
Neither radical can be simplified further.
\(3\sqrt 7 \left( {5\sqrt 2 - 2} \right) = 15\sqrt {14} - 6\sqrt 7 \)