## zaphod 3 years ago Simplify

1. zaphod

$\frac{\sqrt{6}}{\sqrt{2}} + \frac{3}{\sqrt{3}} + \frac{\sqrt{15}}{\sqrt{5}} +\frac{\sqrt{18}}{\sqrt{6}}$

2. waterineyes

Remember one thing: $\large \color{green}{\frac{\sqrt{x}}{\sqrt{y}} = \sqrt{\frac{x}{y}}}$

3. waterineyes

So for first term apply this formula... and tell me what do you get..??

4. waterineyes

@mathslover will suggest you to take the rationalization process I guess..

5. mathslover

$\large{\frac{\sqrt{6}}{\sqrt{2}}=\sqrt{\frac{6}{2}}}$ $\large{\sqrt{6}=\sqrt{3}}$ $\large{\frac{3}{\sqrt{3}}}$Now rationalizing the above expression

6. waterineyes

Every term will contain 3 after solving Strange WOW..

7. zaphod

yes i get it, but then how do i simplify later

8. mathslover

sorry i meant : $$\frac{\sqrt{6}}{\sqrt{2}}=\sqrt{3}$$

9. zaphod

yes there are three terms like that and the other one 3/root 3

10. waterineyes

What do you get show us first..

11. mathslover

|dw:1342950785620:dw|

12. zaphod

root 3 + root 3 + root 3 + 3/ root 3

13. mathslover

Yes right

14. waterineyes

Oh sorry..

15. waterineyes

Take the LCD..

16. zaphod

then it becomes 3 root 3 + 3/root 3

17. waterineyes

LCD = root(3)

18. zaphod

i get it thanks :)

19. zaphod

we have to rationalize later :)

20. waterineyes

Take the LCM and then we will do rationalization..

21. waterineyes

Yes you are absolutely correct @zaphod

22. zaphod

thanks alot :) guys

23. mathslover

Now rationalizing $$\huge{\frac{3}{\sqrt{3}}}$$ = $$\huge{\frac{3*\sqrt{3}}{\sqrt{3}*\sqrt{3}}}$$ $\huge{\frac{\sqrt{3}\cancel{3}^1}{\cancel{3}^1}}$ $\huge{\sqrt{3}}$

24. waterineyes

Or if you take rationalization process first then you need not to take LCD..

25. waterineyes

|dw:1342951138950:dw|

26. waterineyes

Did you understand how to do this?? @zaphod

27. zaphod

28. waterineyes

My question is not about the answer.. I said did you get how to do this??

29. zaphod

yes i got it

30. waterineyes

That is nice..