Saiyan one year ago 9. what is the simplest form of the equation? square root of 2 + square root of 5/square root of 2 - square root of 5.

1. Saiyan

Anyone help plz.

2. sohailiftikhar

Do mean that $\sqrt{2}+\sqrt{5}\div \sqrt{2}-\sqrt{5}$

3. Saiyan

yes

4. sohailiftikhar

ok

5. Saiyan

I just don't know the steps to work through it.

6. sohailiftikhar

Do you want factorize it ?

7. Saiyan

do u mean factor it

8. sohailiftikhar

you can multiply it with $\sqrt{2}.\sqrt{5}$

9. sohailiftikhar

to make it simple

10. Saiyan

$so \sqrt{2} \times \sqrt{5} which is \sqrt{10}$

11. Saiyan

or do i multiply the equation times sqrt(5)

12. DanJS

Is it supposed to be.. $\frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} -\sqrt{5} }$

13. Saiyan

yes

14. sohailiftikhar

$dude when you will multiply then \sqrt{2}*\sqrt{2} will become 2 and vice versa$

15. DanJS

multiply the fraction by.. $\frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} + \sqrt{5} }$

16. DanJS

$(\frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} -\sqrt{5} }) * (\frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} +\sqrt{5} }) =$

17. DanJS

no more roots in the denominator after that

18. sohailiftikhar

yes

19. DanJS

$=\frac{ 2 + 2\sqrt{2}\sqrt{5} + 5 }{ 2 - 5 }$

20. DanJS

$=\frac{ 7 + 2\sqrt{2}\sqrt{5} }{ -3 }$ that about it

21. sohailiftikhar

yeah!

22. Saiyan

so you just multiply the whole equation by the numerator

23. DanJS

24. DanJS

+ to -, or, - to +

25. sohailiftikhar

yes you can but you have to multiply the both sides

26. DanJS

you are just multiplying the fraction by 1

27. DanJS

$\frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} + \sqrt{5} }=1$

28. sohailiftikhar

if you want to remove the numerator then multiply the both sides of equation with it

29. Saiyan

$=7+2\sqrt{2}√5/−3$ is the answer

30. sohailiftikhar

yes

31. Saiyan

ok thx guys

32. sohailiftikhar

no problem dude