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## pratu043 2 years ago How do you find the rationalising factor of root2 + root7 - root10?

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1. pratu043

|dw:1344951900463:dw|

2. mathslover

multiply that by its conjugate @pratu043 what do you get?

3. pratu043

By conjugate you mean: |dw:1344952032255:dw|

4. mathslover

$\large{(\sqrt{2}+\sqrt{7}-\sqrt{10})(\sqrt{2}+\sqrt{7}+\sqrt{10})=?}$

5. mathslover

|dw:1344952080072:dw|

6. mathslover

@pratu043 what do you get by multiplying that.. ?

7. pratu043

How do you find the conjugate?

8. pratu043

I only know how to find for binomial surds.

9. mathslover

@pratu043 let the expression given be like this: $\large{(\sqrt{2}+\sqrt{7})-(\sqrt{10})}$

10. mathslover

I meant to say that: a+b-c = (a+b)-(c) right?

11. pratu043

yes

12. mathslover

|dw:1344952309566:dw|

13. pratu043

|dw:1344952351465:dw| What do you do with - root10?

14. pratu043

|dw:1344952415376:dw| sorry

15. mathslover

ok leave that for once... what will be the conjugate of a+b ?

16. pratu043

a-b

17. mathslover

right so let a = c+d and b = b now can u tell me what will be the new conjugate? : (c+d)+(b) conjugate = ?

18. pratu043

(c+d) - (b)

19. mathslover

right so what will be the conjugate of : $\large{(\sqrt{2}+\sqrt{7})-(\sqrt{10})}$

20. pratu043

|dw:1344952630671:dw| ok, I got the conjugate part.

21. mathslover

right now : multiply this conjugate with original expression

22. pratu043

|dw:1344952686106:dw| right?

23. mathslover

good so we have: $\large{2\sqrt{14}-1}$ now:(√2 + √7 - √10)[(√2 + √7 + √10) (2√14 + 1)] do this

24. pratu043

|dw:1344952926110:dw|

25. pratu043

But why should we do this?

26. mathslover

it is a step towards the answer

27. mathslover

also try to check that out pratu that u did: can that be more simplified?

28. mathslover

@pratu043 you there?

29. pratu043

sorry yes i am there.

30. pratu043

do you mean that we should try and convert the irrationals in that expression to mixed surds?

31. mathslover

yes

32. pratu043

I think I can handle it on my own now, thanks!!

33. mathslover

(√2 + √7 - √10)[(√2 + √7 + √10) (2√14 + 1)] $\large{(\sqrt{2}+\sqrt{7}-\sqrt{10})(\sqrt{2}+\sqrt{7}+\sqrt{10})(2\sqrt{14}+1)}$ $\large{(9+2\sqrt{14}-10)(2\sqrt{14}+1)=(2\sqrt{14}-1)(2\sqrt{14}+1)=56-1=55}$

34. mathslover

nice to hear best of luck

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