Example 1
Completion requirements
| Example 1 |
Simplify \(\frac{3}{{\sqrt 5 }}\).
To eliminate \(\sqrt 5\) from the denominator, you must multiply it by \(\sqrt 5\). If you were just to multiply the denominator by \(\sqrt 5\), you would change the expression. To overcome this issue, multiply the numerator by \(\sqrt 5\) as well.
Notice that the exponent on the 5, in the second line of the solution, is now the same as the index of the radical.
\(\begin{align}
\frac{3}{{\sqrt 5 }} \times 1 &= \frac{3}{{\sqrt 5 }}\cdot \frac{{\sqrt 5 }}{{\sqrt 5 }} \\
&= \frac{{3\sqrt 5 }}{{\sqrt {5^2 } }} \\
&= \frac{{3\sqrt 5 }}{5} \\
\end{align}\)
\frac{3}{{\sqrt 5 }} \times 1 &= \frac{3}{{\sqrt 5 }}\cdot \frac{{\sqrt 5 }}{{\sqrt 5 }} \\
&= \frac{{3\sqrt 5 }}{{\sqrt {5^2 } }} \\
&= \frac{{3\sqrt 5 }}{5} \\
\end{align}\)
Notice that the exponent on the 5, in the second line of the solution, is now the same as the index of the radical.