Example 6
Completion requirements
| Example 6 |
Write \(2r\sqrt{15}\) as an entire radical.
Step 1: Move the coefficient into the radicand by applying an exponent equal to the index of the radical.
\(2r\sqrt{15} = \sqrt{(2r)^2} \cdot \sqrt{15}\)
Step 2: Because the index values of the two radicals are equal, multiply the radicands together, combining them into one radical.
\(\sqrt{(2r)^2} \cdot \sqrt{15} = \sqrt{2^2 \cdot r^2 \cdot 15}\)
Step 3: Simplify.
\(\begin{align}
\sqrt{2^2 \cdot r^2 \cdot 15} &= \sqrt{{4 \cdot r^2 \cdot 15}} \\
&= \sqrt{60r^2} \\
\end{align}\)
Therefore, \(2r\sqrt{15} = \sqrt{60r^2}\).
\(2r\sqrt{15} = \sqrt{(2r)^2} \cdot \sqrt{15}\)
Step 2: Because the index values of the two radicals are equal, multiply the radicands together, combining them into one radical.
\(\sqrt{(2r)^2} \cdot \sqrt{15} = \sqrt{2^2 \cdot r^2 \cdot 15}\)
Step 3: Simplify.
\(\begin{align}
\sqrt{2^2 \cdot r^2 \cdot 15} &= \sqrt{{4 \cdot r^2 \cdot 15}} \\
&= \sqrt{60r^2} \\
\end{align}\)
Therefore, \(2r\sqrt{15} = \sqrt{60r^2}\).