## anonymous one year ago Rationalize the denominator and simplify.

1. anonymous

2. AbdullahM

Hi, welcome to OpenStudy.

3. anonymous

thanks

4. AbdullahM

To rationalize the denominator, you must multiply the numerator and denominator by the conjugate of the denominator. What is the conjugate of $$\sqrt{a}-2\sqrt{y}$$?

5. anonymous

you would just switch the subtraction to addition right?

6. anonymous

how did you make that square root symbol

7. AbdullahM

It's called latex. $$\sqrt{a}$$ That's the code to do it. You can also use the equation button to do it easier :)

8. anonymous

ok cool so wouldnt it be

9. anonymous

$\sqrt{a}+2\sqrt{y}$

10. AbdullahM

Correct!

11. AbdullahM

So now, lets do the multiplication. $$\Large\frac{\sqrt{a}+2\sqrt{y}}{\sqrt{a}-2\sqrt{y}}\times \frac{\sqrt{a}+2\sqrt{y}}{\sqrt{a}+2\sqrt{y}}=?$$

12. AbdullahM

Hint: $$\sf\Large (x+y)(x+y)=x^2+2xy+y^2$$ $$\sf\Large (x+y)(x-y)=x^2-y^2$$

13. anonymous

you lost me

14. AbdullahM

Ok, lets multiply the numerators first. $$\sf\Large (\sqrt{a}+2\sqrt{y})\times (\sqrt{a}+2\sqrt{y})=?$$

15. AbdullahM

Use the formula I gave you above.

16. anonymous

$\sqrt{a^2}+4\sqrt{y^2}$

17. anonymous

?

18. AbdullahM

No...

19. AbdullahM

$$\sf\Large (\sqrt{a}+2\sqrt{y})\times (\sqrt{a}+2\sqrt{y})=?$$ Use the formula: $$\sf\Large (x+y)\times (x+y)= x^2+2xy+y^2$$ remember: x, y, a, and b are all variables.

20. anonymous

im lost

21. anonymous

@Lyralei can you help me

22. AbdullahM

Where are you lost at?