anonymous 4 years ago Simplify the following radicals by rationalizing the denominators.

1. anonymous

one sec i am posting it.

2. anonymous

$\frac{x-y}{\sqrt{x}+\sqrt{y}}$

3. 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}}$

4. 2bornot2b

Now multiply those, you will have removed the radical sign from the denominator.

5. anonymous

how do i multiply them?

6. 2bornot2b

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7. anonymous

Then i simplify? or no?

8. 2bornot2b

Actually you don't need to multiply the numerator, $\frac{\cancel{(x-y)}({\sqrt{x}-\sqrt{y}})}{\cancel{x-y}}$

9. anonymous

So all you have to do is multiply the denominator and that will be the answer?

10. 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?

11. 2bornot2b

Did I puzzle you? Should I write down the whole thing again, in a concise way?

12. anonymous

You puzzled me sorry haha :/ I am terrible at math.

13. 2bornot2b

Ok, then I am writing down the whole thing in a better way....

14. 2bornot2b

You were given with the following expression $\frac{x-y}{\sqrt{x}+\sqrt{y}}$ right?

15. anonymous

Correct.

16. 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 $\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}$

17. 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?

18. anonymous

Yes it is clear. I just do not know how to multiply correctly?

19. 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}}$

20. anonymous

so the answer is the last part of that problem?

21. 2bornot2b

The answer is $\sqrt{x}-\sqrt{y}$

22. anonymous

oh sorry didn't mean to put () and that is simpler then it looks i guess i was just over thinking it.

23. 2bornot2b

Did you understand?

24. anonymous

yes i did thanks!