same number is like multiplying by 1, so you're not really changing the fraction. For this example, the number to multiply by is the square root of 2.
![portable network graphic file16 -65925200](../aaextension/image-Set-6/portable_network_graphic_file16.png)
When you do this, you get: .
![portable network graphic file17 -25108184](../aaextension/image-Set-6/portable_network_graphic_file17.png)
Since the square root of 4 is 2, we can simplify one more step, leaving the answer without a radical in the denominator. .
![portable network graphic file18 Dup 1 -89990880](../aaextension/image-Set-6/portable_network_graphic_file18-Dup-1.png)
Let's try one more example.
Simplify: .
![portable network graphic file19 -74066128](../aaextension/image-Set-6/portable_network_graphic_file19.png)
First,
we use the quotient rule to simplify the fraction. .
![portable network graphic file20 -66543884](../aaextension/image-Set-6/portable_network_graphic_file20.png)
Then simplify, if possible. .
![portable network graphic file20 -95180224](../aaextension/image-Set-6/portable_network_graphic_file20.png)
Return the fraction to one containing a square root in the numerator and one in the denominator in order to rationalize the denominator. .
Multiply the numerator and denominator by the square root of 10. .
![portable network graphic file22 -23803388](../aaextension/image-Set-6/portable_network_graphic_file22.png)
![portable network graphic file23 -89020128](../aaextension/image-Set-6/portable_network_graphic_file23.png)
The square root of 100 can be simplified to 10. .
![portable network graphic file24 -80014824](../aaextension/image-Set-6/portable_network_graphic_file24.png)
Since there is a 5 and a 10 outside the radical symbols, they can be reduced to give the final answer of: .
![portable network graphic file25 -41795968](../aaextension/image-Set-6/portable_network_graphic_file25.png)
Lesson Summary
In order to simplify square roots of quotients, we use the quotient rule, which says that if you have a fraction with a radical in both the numerator and denominator, they can be simplified by placing them both under the same radical .
symbol. If the fraction itself cannot be simplified, the problem is still not completed unless there is no square root in the denominator of the fraction. To remove a radical from the denominator, you must use a process called 'rationalizing the denominator.' This process will not change the value of your expression but will help to rewrite it without using a square root in the denominator of the fraction. .