## anonymous 4 years ago How would you simplify the square root of 45x^9

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1. mayankdevnani

first, 45=9*5 square root of 9=3

2. mayankdevnani

ok

3. anonymous

Ok, I've got that but the exponents are driving me crazy!!

4. calculusfunctions

Please teach. Do not give out solutions and hints @TheViper

5. TheViper

ok @calculusfunctions thanx:)

6. TheViper

@harrisc1221 first find the factors of 45

7. anonymous

I've got that but I am so confused on how to factor the variables and exponents.

8. mayankdevnani

|dw:1350552721744:dw|

9. mayankdevnani

am i right @calculusfunctions

10. calculusfunctions

@harrisc1221 square root and square are inverse operations. In other words, the square root and the square undo each other. For example, if the square of 9 is 81, then the square root of 81 is 9. Understand so far before I continue.

11. anonymous

Ok

12. TheViper

$\large{\sqrt{45x^9}=\sqrt{5\times5\times3\times x\times x \times x\times x\times x\times x\times x\times x\times x}}$ $\Large{=5\times x\times x\times x\times x\sqrt{3\times x}=5x^4\sqrt{3x}}$

13. calculusfunctions

@mayankdevnani yes but you have to ask yourself if the student who is learning understands what you did and more importantly why you did what you did. This is why it's important to allow the student to arrive at the solutions themselves by guiding them, rather than simply saying here, this is how you answer this question. The student may understand this particular problem then but that doesn't help them solve future problems. A teachers job is to teach, not say, oh here let me solve it for you.

14. mayankdevnani

ok but my answer is right

15. anonymous

Ok, so can you teach it to me calculusfunctions??

16. calculusfunctions

@TheViper yet you did it again.

17. calculusfunctions

Yes @harrisc1221

18. anonymous

Ugh!!! I just need help figuring out how to simplify this problem!!!!

19. calculusfunctions

@harrisc1221 I was typing up a lesson for you and my comp lost the connection so allow me a few minutes to type it up again. Thanks.

20. anonymous

Thank You @calculusfunctions

21. anonymous

The actual assignment is multiplying radicals, but I can multiply them I just can't simplify them if they have variables and exponents.

22. calculusfunctions

$\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$ Example:$\sqrt{54x ^{5}}=\sqrt{54}\sqrt{x ^{5}}$Simplify each square root factor. First$\sqrt{54}$The greatest perfect square 54 is divisible by is 9. Thus$\sqrt{54}=\sqrt{9}\sqrt{6}=3\sqrt{6}$Next simplify$\sqrt{x ^{5}}$To find the square root of a variable, we divide the exponent by 2. Thus find the closest exponent that is divisible by 2. In our example the closest even number to 5 is 4. Thus$\sqrt{x ^{5}}=\sqrt{x ^{4}}\sqrt{x}=x ^{2}\sqrt{x}$Now$\sqrt{54x ^{5}}=(3\sqrt{6})(x ^{2}\sqrt{x})=3x ^{2}\sqrt{6x}$Understand @harrisc1221 ?

23. calculusfunctions

@harrisc1221 sorry it took longer because I lost the connection again.

24. calculusfunctions

Now @harrisc1221 could you please show me your solution if you understood so that I may see that you have the correct answer.

25. anonymous

i've got 3*3*5*x^3*x^3

26. calculusfunctions

@Mpost1994 That is what I meant by teaching. As for your comment above, you're clearly not a psychic because FYI I am a teacher who loves teaching so much that I devote almost all my free time to help as many people as I can on this site and others. I would appreciate it if you did not waste anymore of mine and others valuable time.

27. calculusfunctions

28. anonymous

No, it's what I have so far. I don't know how to write it out in the correct format @calculusfunctions

29. calculusfunctions

@harrisc1221 did you understand the lesson along with the example I gave?

30. anonymous

Some of it said there was a path processing error

31. calculusfunctions

Obviously @Mpost1994 you have no respect for teachers.

32. anonymous

math*

33. anonymous

Can you all battle it out somewhere else, I came here because I am having trouble with this and the bickering back and forth is not making it any better!!!

34. calculusfunctions

I'm sorry @harrisc1221 I can't teach wile @Mpost1994 continues to be disruptive and obnoxious. @harrisc1221 let me know when he's gone.

35. anonymous

I am leaving now. Sorry for saying something on your question post list. Bye now.

36. anonymous

The least you could do is have respect for someone else!!!! I am the one that is having trouble with math and if you have a problem with what someone is saying then send them a message, but DON'T litter my message board with this crap!!

37. anonymous

38. anonymous

I could always postpone bed and keep going.

39. anonymous

If you're not willing to help I suggest you get off my question post!!! Gah, there is something called respect and you need to know what it is!! I came here as a last resort but unfortunately I can't even get any help here. So thank you for being a douchebag!!! I hope you're happy, because I am pissed!!!!!!

40. terenzreignz

hey, if I might interrupt? I'm sorry if I disrupt @calculusfunctions line of thought, but perhaps it might be easier to see things in terms of exponents?

41. anonymous

Ok, what do you mean by that @terenzreignz

42. terenzreignz

Well, use laws of exponents to your advantage... Such as... $(mn)^{p}=m^{p}n^{p}$$(m^{p})^{q}=m^{pq}$$\sqrt{m}=m^{\frac{1}{2}}$

43. calculusfunctions

@terenzreignz go ahead because of @Mpost1994 I can't think anyway but as to your comment I did explain in terms of exponents.

44. calculusfunctions

*using exponents. Did you not read the lesson I posted above?

45. anonymous

Am i the only one that keeps having the [math processing error] on their screen?

46. mathslover

@harrisc1221 try to press ctrl+F5

47. calculusfunctions

I've never ever been so disrespected by any student as I have today by @Mpost1994

48. anonymous

It's still not showing up @mathslover

49. mathslover

@Mpost1994 , : as per openstudy code-of-conduct ( http://openstudy.com/code-of -conduct ) : Don't just provide the answer to a problem when someone else is in the middle of helping! But if you want to help, by all means, join in! So, I request you to NOT interrupt between the answer process of a user to the asker , I hope you will value the above point and will not devalue the question/answer process from now. Thanks! Oh btw , @harris1994 and @calculusfunctions I am impressed with both of your's discussion and interaction, this is the perfect use of OpenStudy .

50. calculusfunctions

@harrisc1221 $\sqrt{45x ^{9}}=\sqrt{45}\sqrt{x ^{9}}$Correct?

51. calculusfunctions

I'm not going to let the low lives like @Mpost 1994 detract me from teaching. He thinks he got to me but then that would like letting a terrorist win. Therefore I'm going to continue and not let scum bother me.

52. calculusfunctions

So @harrisc1221 let's continue shall we?

53. anonymous

YES! @calculusfunctions

54. calculusfunctions

So first let's simplify$\sqrt{45}$first. Based on the example I gave, what do you think we should do first? Did you even read my example carefully?

55. anonymous

we should simplify the square root of 54 first @calculusfunctions

56. calculusfunctions

Yes so then read the steps I explained to do that and simplify $\sqrt{45}$

57. anonymous

which would be 3*3*5 @calculusfunctions

58. calculusfunctions

Yes the greatest perfect square that 54 is divisible by is 9. Thus??

59. anonymous

I'm still having a hard time reading your input because of the math processing error, sorry.

60. calculusfunctions

$\sqrt{45}=\sqrt{9}\sqrt{5}=?$

61. calculusfunctions

I'm not sure why you're seeing error. I'm not experiencing the same issue.

62. anonymous

$\sqrt[3]{5}$

63. anonymous

I don't know either I have pushed ctrl and F5

64. calculusfunctions

LOL I think you mean$3\sqrt{5}$

65. anonymous

I can only see you're reply if you tag me in the post for some reason @calculusfunctions

66. calculusfunctions

@harrisc1221 you mean$3\sqrt{5}$Do you see it now?

67. anonymous

lol yes

68. calculusfunctions

Sorry @harrisc1221 but this @Mpost piece of disrespectful trash still keeps bothering me. The problem is that the moderators aren't around at the moment so he seem to taking advantage. But like I said we don't let terrorists win so let's continue.

69. calculusfunctions

@harrisc1221 next we have$\sqrt{x ^{9}}$The square root of a variable is found by dividing the the exponent of the variable by 2. This implies that the exponent must be even Thus what is the closest even number to 9?

70. anonymous

8

71. calculusfunctions

@harrisc1221 correct so then$\sqrt{x ^{9}}=?$

72. anonymous

wow alot has gone on here lol @calculusfunctions u r a great math teacher dont let any one tell you diffrent

73. anonymous

x^8*x

74. anonymous

nice work here @calculusfunctions just the way it should be

75. calculusfunctions

Thank you @mikala1 It's because of decent, respectful, hardworking, motivated students like yourself, @harrisc1221, @mathslover, and many others that I will never stop and I refuse to allow a few individuals such as @Mpost 1994 to be problematic.

76. anonymous

this is actually an excellent example that solving by examples is a very efficient way of teaching

77. calculusfunctions

@lgbasallote thank you for your kind words. I appreciate the respect and the support from students like you, as I mentioned in the above comment. Thank you!!!!

78. anonymous

even more efficient than actually telling the first few steps of the solution P.S. <----not a student

79. calculusfunctions

@harrisc1221 yes$\sqrt{x ^{9}}=\sqrt{x ^{8}}\sqrt{x}=?$

80. calculusfunctions

LOL @lgbasallote I apologize. I didn't know you were not a student. Are you also a teacher?

81. anonymous

Ok, so now I am lost after that last step

82. anonymous

i would assume "also" means you're a teacher? and yes, i am a liberal arts professor

83. calculusfunctions

@harrisc1221 What is $\sqrt{x ^{8}}=?$What did I say earlier about taking the square root of a variable?

84. anonymous

It is divided by 2

85. calculusfunctions

@harrisc1221 what is divided by 2?

86. anonymous

the exponent

87. calculusfunctions

@lgbasallote you assume correctly sir! I math and physics.

88. anonymous

You would dived 8 by 2 and get 4

89. calculusfunctions

@harrisc1221 $\sqrt{x ^{8}}=?$

90. anonymous

That is what I meant, I can't get the equation function to work right

91. anonymous

then x = x

92. calculusfunctions

@harrisc1221 then$\sqrt{x ^{9}}=\sqrt{x ^{8}}\sqrt{x}=?$

93. calculusfunctions

@mikala1 I guess he's gone for now. He did message saying that he would have to go soon. I have to go in a bit as well but is there anything I can help you with before I do?

94. anonymous

no i was just watching u do ur leaason so i could learn

95. calculusfunctions

@mikala1 that's great. Did you learn anything and are you good with those linear equations now?

96. anonymous

just a little im not that far yet lol im only in 9 th grade

97. terenzreignz

@calculusfunctions Your patience is inspiring... It comes as no surprise that you're into teaching :D

98. calculusfunctions

@mikala1 yes i already knew you were in Grade 9 because you were studying linear equations.

99. calculusfunctions

@terenzreignz Thank you. I appreciate the encouragement.

100. anonymous

lol just a little but i shall have more question next week for u

101. calculusfunctions

@mikala1 of course! Whenever you need me, simply let me know.

102. anonymous

ok sheldon

103. anonymous

loll

104. calculusfunctions

Haha! I see that I remain a mystery to you. LOL. But seriously I appreciate the compliment, although I don't see myself as being as intelligent as Sheldon.

105. anonymous

u r for real lol and hes real not that smart in dating world lol

106. calculusfunctions

LOL. I love that show!! My ringtone is the theme song.

107. calculusfunctions

Anyway I have to go now but you like I said, you let me know if you want my help. Alright?

108. anonymous

lol u rwaly do sound like him thogh n ok

109. anonymous

have a great day

110. calculusfunctions

You too! Bye!

111. anonymous

Yeah still needing help with help with this