anonymous
  • anonymous
Simplify the following radicals by rationalizing the denominators.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
one sec i am posting it.
anonymous
  • anonymous
\[ \frac{x-y}{\sqrt{x}+\sqrt{y}} \]
2bornot2b
  • 2bornot2b
\[\frac{x-y}{\sqrt{x}+\sqrt{y}}\]\[\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\]

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More answers

2bornot2b
  • 2bornot2b
Now multiply those, you will have removed the radical sign from the denominator.
anonymous
  • anonymous
how do i multiply them?
2bornot2b
  • 2bornot2b
|dw:1328019438214:dw|
anonymous
  • anonymous
Then i simplify? or no?
2bornot2b
  • 2bornot2b
Actually you don't need to multiply the numerator, \[\frac{\cancel{(x-y)}({\sqrt{x}-\sqrt{y}})}{\cancel{x-y}}\]
anonymous
  • anonymous
So all you have to do is multiply the denominator and that will be the answer?
2bornot2b
  • 2bornot2b
In all similar problems as this one, just multiply the numerator and the denominator with the conjugate of the denominator, just as I did. And then you need to simplify. But in this problem, one of the terms of the numerator gets cancelled. Did you understand?
2bornot2b
  • 2bornot2b
Did I puzzle you? Should I write down the whole thing again, in a concise way?
anonymous
  • anonymous
You puzzled me sorry haha :/ I am terrible at math.
2bornot2b
  • 2bornot2b
Ok, then I am writing down the whole thing in a better way....
2bornot2b
  • 2bornot2b
You were given with the following expression \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\] right?
anonymous
  • anonymous
Correct.
2bornot2b
  • 2bornot2b
Now I multiply both the numerator and the denominator with the conjugate of the dimnomnator i.e. \[\sqrt{x}-\sqrt{y}\] So the expression gets converted to \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\]
2bornot2b
  • 2bornot2b
Is it clear till this step? I can multiply something to the numerator and as well as to the denominator since they can be cancelled Is it clear?
anonymous
  • anonymous
Yes it is clear. I just do not know how to multiply correctly?
2bornot2b
  • 2bornot2b
So now I can say \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\]\[=\frac{(x-y)({\sqrt{x}-\sqrt{y}})}{\sqrt{(x)^2}+\sqrt{(y)^2}}\]\[=\frac{\cancel{(x-y)}({\sqrt{x}-\sqrt{y}})}{\cancel{x-y}}\]
anonymous
  • anonymous
so the answer is the last part of that problem?
2bornot2b
  • 2bornot2b
The answer is \[\sqrt{x}-\sqrt{y}\]
anonymous
  • anonymous
oh sorry didn't mean to put () and that is simpler then it looks i guess i was just over thinking it.
2bornot2b
  • 2bornot2b
Did you understand?
anonymous
  • anonymous
yes i did thanks!

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