Example 2
Completion requirements
| Example 2 |
Simplify the expression \(\sqrt {20} + 5\sqrt 5 \).
Upon initial inspection, the expression may appear to already be fully simplified. While the index values are equal, the radicands are not equal. But, notice that \(\sqrt{20}\) is not in its most simplified form.
Step 1: If possible, simplify individual radicals.
\(\begin{align}
\sqrt {20} + 5\sqrt 5 &= \sqrt {4\cdot 5} + 5\sqrt 5 \\
&= 2\sqrt 5 + 5\sqrt 5 \\
\end{align}\)
Step 2: Collect like terms to simplify the expression.
\(\begin{align}
2\sqrt 5 + 5\sqrt 5 &= \left( {2 + 5} \right)\sqrt 5 \\
&= 7\sqrt 5 \\
\end{align}\)
Step 1: If possible, simplify individual radicals.
\(\begin{align}
\sqrt {20} + 5\sqrt 5 &= \sqrt {4\cdot 5} + 5\sqrt 5 \\
&= 2\sqrt 5 + 5\sqrt 5 \\
\end{align}\)
Step 2: Collect like terms to simplify the expression.
\(\begin{align}
2\sqrt 5 + 5\sqrt 5 &= \left( {2 + 5} \right)\sqrt 5 \\
&= 7\sqrt 5 \\
\end{align}\)