Example 4
Completion requirements
| Example 4 |
Simplify \(\sqrt{8w^3q^2}\).
Step 1: Rewrite the radicand as a product of factors, looking specifically for factors that are perfect squares.
\(\begin{align}
\sqrt{8w^3 q^2} &= \sqrt {4w^2q^2\cdot 2w} \\
&= \sqrt {2^2w^2q^2\cdot 2w} \\
\end{align}\)
Step 2: Rewrite the radical as a product of the perfect square radicals and the non-perfect square radicals.
\(\sqrt{2^2w^2q^2\cdot 2w} = \sqrt {2^2} \cdot \sqrt{w^2}\cdot \sqrt{q^2 }\cdot \sqrt{2w}\)
Step 3: Simplify.
\(\sqrt{2^2 }\cdot \sqrt{w^2 }\cdot \sqrt{q^2}\cdot \sqrt{2w} = 2qw\sqrt {2w}\)
Therefore, \(\sqrt {8w^3q^2} = 2qw\sqrt{2w} \)
\(\begin{align}
\sqrt{8w^3 q^2} &= \sqrt {4w^2q^2\cdot 2w} \\
&= \sqrt {2^2w^2q^2\cdot 2w} \\
\end{align}\)
Step 2: Rewrite the radical as a product of the perfect square radicals and the non-perfect square radicals.
\(\sqrt{2^2w^2q^2\cdot 2w} = \sqrt {2^2} \cdot \sqrt{w^2}\cdot \sqrt{q^2 }\cdot \sqrt{2w}\)
Step 3: Simplify.
\(\sqrt{2^2 }\cdot \sqrt{w^2 }\cdot \sqrt{q^2}\cdot \sqrt{2w} = 2qw\sqrt {2w}\)
Therefore, \(\sqrt {8w^3q^2} = 2qw\sqrt{2w} \)