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Dividing Radical Expressions

In this video, we are going to divide radical expressions.

One simple example is:
\frac{\sqrt{25}}{\sqrt{9}}
By simplifying the numerator and the denominator, we now have \frac{5}{3}

A slightly more difficult problem would be:
\frac{\sqrt{50}}{\sqrt{18}}
Just like the other problem, first find perfect square factors for each expression
\frac{\sqrt{25}\times\sqrt{2}}{\sqrt{9}\times\sqrt{2}}
Simplify each expression
\frac{5\sqrt{2}}{3\sqrt{2}}
And the final answer is \frac{5}{3}

If the expression has a radical in the denominator and a rational number in the numerator, then it is necessary to rationalize the fraction.
For example:
\frac{3}{\sqrt{10}}
Multiple the denominator to both the numerator and the denominator. Like terms cancel each other out so the final answer is:
\frac{3\times\sqrt{10}}{\sqrt{10}\times\sqrt{10}}
\frac{3\sqrt{10}}{10}