## anonymous 3 years ago Multiply and simplify Radical Expression 1/2√5(1 1/2√20)

1. anonymous

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2. anonymous

Hi I got the answer of 7/2√5 but when I do it I get something different.

3. anonymous

okay so lets write that a little prettier to deal with:${{1\over2}\sqrt{5}}\times{1~{1\over2}\sqrt{20}}~~\implies~~{{1\over2}\sqrt{5}}\times{{3\over2}\sqrt{20}}~~\implies~~{\sqrt{5}\over2}\times{3\sqrt{20}\over2}$now that that looks a little better, let's solve:${{\sqrt{5}\times3\sqrt{20}}\over2}={3\sqrt{100}\over2}$because 5 x 20 = 100$3(10)\over2$i think you've got it from here :)

4. anonymous

oh i meant to write $3(10)\over4$sorry

5. anonymous

I'm a bit lost I have to simplify this so would'nt 1 1/2√20 be 2 3/2√5

6. anonymous

$1 {1\over2} = {3\over2}$$\sqrt{20}= 2\sqrt{5}$${3\over2}\times{2\over1}\sqrt{5}~~=~~{3\over\cancel{2}}\times{\cancel{2}\over1}\sqrt{5}~~=~~\large3\sqrt{5}$

7. anonymous

but the answer comes out to $\frac{ 7 }{ 2 }\sqrt{5}$

8. anonymous

and where are you getting this from?

9. anonymous

Our teacher placed the answer as $\frac{ 7 }{ 2 }\sqrt{5}$

10. anonymous

I didn't get this answer either this is why it's confusing

11. anonymous

1/2 times 3/2 = 3/4 sqrt 5 times sqrt 20 = sqrt100 = 10 3/4 times 10 = 7.5 i dont know what your teacher was doing, maybe you copied the question wrong

12. anonymous

No it's printed on my paper

13. anonymous

then im really not sure

14. anonymous

I appreciate your help Thank you yummydum

15. anonymous

no problem :)

16. anonymous

I got as my final answer $\frac{ 3 }{ 4 }\sqrt{5}$ this is why it was confusing

17. anonymous

I had a person help me don't I don't believe it's correct here is why unless I'm wrong

18. saifoo.khan

Alright so i read the whole problem. Where are you stuck? We should get 15/2.

19. anonymous

$1\frac{ 1 }{ 2 }\sqrt{20}$ would be $\frac{ 3 }{ 2 }$ and $\sqrt{20} would be 2$ add both $2\frac{ 3 }{ 2 }\sqrt{5}$

20. anonymous

teacher has an answer of $\frac{ 7 }{ 2 }\sqrt{5}$ could the teacher be wrong

21. saifoo.khan

Yes. Teacher added the sqrt5 by misatke. Or maybe the question you wrote is incorrect.

22. anonymous

question is multiply and simplify $\frac{ 1 }{ 2 }\sqrt{5}\left( 1\frac{ 1 }{ 2 } \sqrt{20}\right)$

23. saifoo.khan

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24. anonymous

Why is this so complicated? I'm lost

25. saifoo.khan

Which step is it that you don't understand?

26. anonymous

how would I multiply $\frac{ \sqrt{5} }{ 2 }\times \frac{ 3*2 }{ 2 }\sqrt{5}$ I thought you multiply numbers not square roots with numbers

27. anonymous

my answer was $\frac{ 3 }{ 4 }\sqrt{5}$ maybe this is wrong

28. saifoo.khan

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29. anonymous

Wouldn't we keep the root? and just multiply getting $\frac{ 15 }{ 2 }\sqrt{5}$

30. saifoo.khan

No ma'am. Whenever it's given: sqrt3 * sqrt3 we will get "3" as answer. The roots cancel out leaving you with ONE three.

31. anonymous

This is how I started $\frac{ 1 }{ 2 }\sqrt{5}(1\frac{1 }{ 2 }\sqrt{20})$ $\frac{ 1 }{ 2 }\sqrt{5}(\frac{3 }{ 2 }\sqrt{5})$ $\frac{ 1 }{ 2 }\times \frac{ 3 }{ 2 }=\frac{ 3 }{ 4 }\sqrt{5}$ I know this isn't corrected but I get this

32. saifoo.khan

How will you simplify sqrt 20?

33. anonymous

that's right it would be 4*5 which 4 goes down to 2 so it would be $2\sqrt{5}$

34. saifoo.khan

^

35. anonymous

I forgot to add that $\frac{ 1 }{ 2 }\sqrt{5}(2\frac{3 }{ 2 }\sqrt{5})$ it would be this correct and mix fractions to improper fractions would be $2\frac{ 3 }{ 2 } would be \frac{ 7 }{ 2 }$ $\frac{ 1 }{ 2 }\sqrt{5}(\frac{ 7 }{ 2 }\sqrt{5})$

36. saifoo.khan

You made a mistake again. :P It's not 2 3/2

37. anonymous

so it's $\frac{ 2 }{ 1 }X\frac{ 3 }{ 2 }$

38. saifoo.khan

No. I think you should redo the problem. Show me yor steps please.

39. anonymous

ok

40. anonymous

$\frac{ 1 }{ 2 }\sqrt{5}(1\frac{ 1 }{ 2 }\sqrt{20})$ $\frac{ 1 }{ 2 }\sqrt{5}(\frac{ 3 }{ 2 } 2\sqrt{5})$ $\frac{ 1 }{ 2 }\sqrt{5}(\frac{ 3 }{ 2 } 2\sqrt{5})$ at this point I'm lost

41. saifoo.khan

Awesome. No the 2's on right cancels out. Right?

42. anonymous

why would it cancel √20 would be 2√5 this is where I'm getting confused

43. anonymous

is 2 canceling with the other 2

44. saifoo.khan

sqrt(20) = sqrt(2*2*5) = 2 sqrt5 Agree?

45. anonymous

yes

46. saifoo.khan

Now the 2 from 2sqrt5 and the w in the denominator on the right canel out

47. anonymous

I'm with you on that

48. saifoo.khan

Right o what are we left with now?

49. anonymous

3√5

50. saifoo.khan

Right. And that is multiplied with..?

51. anonymous

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

52. saifoo.khan

Right now multiply it out.

53. anonymous

$\frac{ 1 }{ 2 }\sqrt{5}\times \frac{ 3 }{ 1 }\sqrt{5}$ Is this looking correct?

54. saifoo.khan

yes

55. anonymous

$\frac{ 3 }{ 2 }\sqrt{5}$

56. anonymous

do I take of the √ and make it $\frac{ 3 }{ 2 }\times \frac{ 5 }{ 1 }=\frac{ 15 }{ 2 }$

57. saifoo.khan

Like a boss. (y)

58. anonymous

Thanks for everything wow :.)

59. anonymous

Good job helping @newatthis !!! @saifoo.khan

60. anonymous

Kudos to @yummydum too!

61. saifoo.khan

@yummydum is useless.

62. anonymous

No she isn't :p

63. anonymous

I'M useless.

64. anonymous

Yummydum isn't. Or you,for that matter.

65. anonymous

Thanks for everything it helps a lot when someone knows how to guide and explain it. :)

66. saifoo.khan

@help123please. believe me. I know her. @newatthis You're welcome. :)

67. anonymous

Well,yes...you've been here longer than me.

68. saifoo.khan

Lol. But no doubt she has a brown brain like me! D:

69. anonymous

O_O

70. anonymous

Yours is a great brain,Saif.

71. anonymous

72. saifoo.khan

And it's brown too!

73. anonymous

Nope it's not.

74. saifoo.khan

I'm brown. Brain is brown too. Dummy is brown too. Hence she has a brown brain too.

75. anonymous

We're prolly weirding @newatthis out. Or at least,I am.

76. anonymous

:P

77. anonymous

'Hence,she has a brown brain too'. Hence. I like that word.

78. saifoo.khan

Lol.

79. anonymous

no I'm just doing math working my brain, or whatever is left. :)

80. anonymous

Saif,I just noticed your smartscore is mine,with the numbers flipped upside down. XD

81. saifoo.khan

Haha. Nice catch.

82. anonymous

IKR.

83. anonymous

*Flips PC upside down* OMGEE I HAVE A 99 SS!

84. saifoo.khan

Lol.

85. anonymous

98% of the time,when typing lol,you're not actually laughing. Did u know? :P

86. saifoo.khan

Make that 99%. I love laughing. It helps in exercising my face muscles. :P

87. anonymous

Lawl.

88. saifoo.khan

;)

89. anonymous

so new question? $2x \sqrt{7}(3x \sqrt{7})$ $2x(3x)\sqrt{7}\sqrt{7}$ $6x(\sqrt{49})$ Would this be correct?

90. anonymous

sorry I just threw this in here

91. anonymous

92. anonymous

2x * 3x = 6x^2 not just 6x and √49 = 7 so now you have 6x^2 * 7 ....which is?

93. anonymous

$42x ^{2}$

94. anonymous

yes