anonymous 5 years ago rationalize denominator : please help 1.) 4/ sqrt. 7p 2.) srqt.98/x 3.) 9/3 sqrt.y 4.) sqrt.7 / sqrt.5 +7

1. anonymous

1.) $4/ \sqrt{7p}$ 2.) $\sqrt{98}/x$ 3.) $9/ 3\sqrt{y}$ 4.) $\sqrt{7}/ \sqrt{5} + 7$

2. anonymous

please hlep , i dont understand them

3. dumbcow

ok the idea is to get the sqrt out of the denominator For 1) multiply by sqrt(7p)/sqrt(7p)

4. dumbcow

sqrt(x) * sqrt(x) = x

5. anonymous

so it would be p ?

6. dumbcow

7p everything within the radical sorry imagine if i said x = 7p ->4*sqrt(7p)/7p that is the rationalised form for the first one

7. dumbcow

For number 4 you have to use a conjugate which is basically the denominator except you flip the sign ->sqrt(5)-7 multiply this on top and bottom by distributing (using FOIL) and the sqrts in denominator will go away

8. dumbcow

number 2 is already rationalised but you can simplify sqrt(98) by factoring out a perfect square number 3 can be done same way as num 1, dont forget to reduce hope this helps

9. anonymous

so how would it be done ?

10. anonymous

and thank you for helping , im just really bad in math

11. dumbcow

which part are you stuck on

12. dumbcow

figure it out??

13. anonymous

all of it , especially foil

14. dumbcow

ok lets look at num 2 since there is no sqrt in denominator, we don't have to do anything there but we can simplify sqrt(98) Factors of 98 = 2*49 =2*7*7 rewrite sqrt(98) as sqrt(2)*sqrt(7)*sqrt(7) remember sqrt(7)*sqrt(7) = 7 leaving 7sqrt(2)

15. anonymous

7sqrt. 2x

16. anonymous

?

17. anonymous

for number one i got : 4sqrt.7p/7p ? correct ?

18. dumbcow

7sqrt(2)/x sorry no the x doesnt change it stays on the bottom

19. dumbcow

correct

20. dumbcow

for num 3 we want to get rid of sqrt(y) by multiplying by sqrt(y) on top and bottom ->9/3sqrt(y) * sqrt(y)/sqrt(y) = 9sqrt(y)/3y Now reduce what does 9/3 reduce to?

21. anonymous

or would 7p cancel itself ?

22. anonymous

to 3

23. dumbcow

correct ohh no the 7p wouldnt cancel because the one on top is inside the sqrt, that is important

24. dumbcow

25. anonymous

oh no your answer for 3 is wrong , it doesnt come out in my exam as an option

26. dumbcow

hmm maybe the sqrt is in the numerator try 3sqrt(y)

27. anonymous

there is no 3 , only 9 sqrt

28. dumbcow

hmm maybe the sqrt is in the numerator try 3sqrt(y)

29. dumbcow

interesting, what are the possible answers they give

30. anonymous

number 3 : A) 9^3 sqrt.y^2 /y b.) 9y c.) 9^3 sqrt. y^2 d.) 9^3 sqrt. y /y

31. dumbcow

and your sure the question was 9/(3sqrt(y))

32. anonymous

yes

33. anonymous

it better view higher above ^^^^ with the equation button

34. anonymous

all the way up^^^^^^^^^^^^^^^^^^^^^^

35. dumbcow

well in that case the answer is 3sqrt(y)/y i'd bet on d) , weird you might have to talk to teacher on this one

36. anonymous

and for the rest of the problems ?

37. dumbcow

38. anonymous

do you know how to solve this though ?

39. dumbcow

rationalise fractions with sq roots? yes i know how to solve those but maybe they're looking for something else look at prev examples and see if it lines up with what i've shown

40. anonymous

correction : $9 / ^{3} \sqrt{y}$

41. anonymous

so it changes everything ?

42. dumbcow

little bit the answer is A think of it now as fractional exponents cube root of y = y^(1/3) to cancel that we multiply top and bottom by y^2/3 ->y^1/3 * y^2/3 = y (add the exponents) leaving (9*y^2/3)/y

43. anonymous

you mean : 9^3 sqrt.y^2 / y ?

44. dumbcow

oh y^2/3 can be written as cube root of y^2

45. anonymous

its the same than ?

46. dumbcow

yes

47. anonymous

thank youuu ! its so complicated to me. and the rest ?

48. dumbcow

oh yes FOIL is just way to remember how to distribute. what is result of (x+2)*(x-3)? _>distribute the x to both the x and -3 ->x*x + x*-3 = x^2 - 3x ->then distribute the 2 to the x and -3 ->2*x + 2*-3 = 2x -6 put it together ->x^2 -3x +2x -6 = x^2 -x -6 make sense?

49. anonymous

is there an easier way ?

50. anonymous

i have to use (x+2)*(x-3) in the equation to cancel out sqrt ?

51. dumbcow

no that was just an example and not really you still have to do the multiplications For this problem we would be multiplying (sqrt(5)+7) * (sqrt(5) - 7)

52. dumbcow

sorry i gotta go the answer is (7sqrt(7) - sqrt(35))/44 try to figure it out on your own by multiplying what i put above for denominator then multiply sqrt(7)*(sqrt(5)-7) for numerator Then at the end you have to distribute a negative by flipping the signs good luck