Example 2
Completion requirements
| Example 2 |
Simplify \(\frac{{6\sqrt 2 }}{{5\sqrt {3b} }}\).
Step 1: Identify just the radical in the denominator.
In this case, \(\sqrt {3b}\) is the radical. Note that you do not multiply by \(5\sqrt{3b}\) because \(5\) is not a radical.
Step 2: Multiply both numerator and denominator by that radical.
Watch for the simplification that can occur after rationalizing the denominator, such as removing a factor of three from both the numerator and the denominator in this example.
In this case, \(\sqrt {3b}\) is the radical. Note that you do not multiply by \(5\sqrt{3b}\) because \(5\) is not a radical.
Step 2: Multiply both numerator and denominator by that radical.
\(\begin{align}
\frac{{6\sqrt 2 }}{{5\sqrt {3b} }} &= \frac{{6\sqrt 2 }}{{5\sqrt {3b} }}\cdot \frac{{\sqrt {3b} }}{{\sqrt {3b} }} \\
&= \frac{{6\sqrt {2 \cdot 3b} }}{{5\sqrt {3^2 b^2 } }} \\
&= \frac{{6\sqrt {6b} }}{{5 \cdot 3b}} \\
&= \frac{{2\sqrt {6b} }}{{5b}} \\
\end{align}\)
\frac{{6\sqrt 2 }}{{5\sqrt {3b} }} &= \frac{{6\sqrt 2 }}{{5\sqrt {3b} }}\cdot \frac{{\sqrt {3b} }}{{\sqrt {3b} }} \\
&= \frac{{6\sqrt {2 \cdot 3b} }}{{5\sqrt {3^2 b^2 } }} \\
&= \frac{{6\sqrt {6b} }}{{5 \cdot 3b}} \\
&= \frac{{2\sqrt {6b} }}{{5b}} \\
\end{align}\)
Watch for the simplification that can occur after rationalizing the denominator, such as removing a factor of three from both the numerator and the denominator in this example.