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Mrfootballman97 2 years ago How do you simplify:

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1. Mrfootballman97

$\sqrt{72}$

2. KonradZuse

Okay so some easy steps to start simplifying.

3. KonradZuse

First you're going to want to try to split that 72 into something you know can factor.

4. KonradZuse

Any idea what 72 can be split into?

5. Mrfootballman97

36?

6. KonradZuse

and what?

7. Mrfootballman97

ohhhhh. Do you mean like 8 times 9?

8. KonradZuse

yes, or like tyou said 36 times what? Your first guess was correct.

9. Mrfootballman97

so then what?

10. Mrfootballman97

or is that the answer? lol

11. KonradZuse

$\sqrt{36 * ?}$

12. Mrfootballman97

2

13. KonradZuse

$\sqrt{36 * 2}$

14. KonradZuse

now can you simplify sqrt(36 or sqrt(2)?

15. KonradZuse

WE don't split it up, so sorry if that last comment is confusing....

16. KonradZuse

WE can just look at each piece now, and determine what's needed....

17. abb0t

You can also use 8 and 9...

18. KonradZuse

yes, we can abb0t.... but this is easier. I was going to show 8 and 9 after.

19. Mrfootballman97

i can simplify 36 into

20. Mrfootballman97

$\sqrt{6 * 6}$

21. KonradZuse

nono, we don't need to simplify it that way. I meant does sqrt(36) or sqrt(2)= anything?

22. Mrfootballman97

oh yeah, 36= 6 and 2= 1.414214562. do i have to simplify 2?

23. KonradZuse

correct so we get $6 \sqrt{2}$ which is our answer.

24. Mrfootballman97

ahhhhhhh thanks a lot

25. KonradZuse

we don't need to simplify 2, we just need to get it into it's simpliest form.

26. KonradZuse

so for example, lets use 8 and 9.

27. KonradZuse

$\sqrt{72} = \sqrt{8 * 9} = 3 \sqrt{ 4 * 2} = 2 *3 \sqrt{2} = 6 \sqrt{2}$

28. KonradZuse

Its' really just trying to take some ugly sqrt thart we cannot solve and split it into things that we can solve for :).

29. Mrfootballman97

i liked the 36 and 2 one better lol. Thanks again!

30. KonradZuse

Yeah, it's easier, but you can see how it can be applied with any set :). Good luck, I hope you understand the concepts.

31. Mrfootballman97

so lets see if i have this:

32. KonradZuse

Sure, throw up a random # and lets see if we can solve.

33. KonradZuse

as long as it's not prime... AHAH..

34. Mrfootballman97

$\sqrt{75} = 5\sqrt{3}$

35. KonradZuse

yes.

36. Mrfootballman97

yaaahooooo

37. Mrfootballman97

ok thanks cya later!

38. KonradZuse

$\sqrt{75} = \sqrt{25 * 3} = 5 \sqrt{3}$

39. KonradZuse

np good luck.

40. Mrfootballman97

Hey here is a new type of problem:

41. Mrfootballman97

$\sqrt{5} \times \sqrt{35}$

42. Mrfootballman97

Think you can do that?

43. KonradZuse

hmm Idk man you're asking a lot here... :p

44. KonradZuse

lets start off basic. Multiply them together, what do we get?

45. KonradZuse

or, if you want, you can split sqrt(35) into 2 parts, and go that way :).

46. Mrfootballman97

well i dont need to get the answer to the equation, i think i just need to simplify it. Its under the section of simplifying

47. Mrfootballman97

so do i just simplify each part?

48. KonradZuse

simplifying is the same thing.

49. KonradZuse

you basically are given an eq, to solve. IT could be multiplication, addition, etc, etc. Then you want to use the elements to combine and form something you are able to simplify and take something out of the sqrt. That is our main objective, to get a real number.

50. KonradZuse

We are doing exactly what we did before, exept we are adding an additional step. Instead of 35 and 5, we had 36 and 2. or 9 and 8(9 * 4 *2)

51. KonradZuse

I guess above I shouldn't have said you shouldn't split them out, because in the end you can, and it doesn't matter.... sqrt(36) * sqrt(2) is the same thing

52. KonradZuse

6 * sqrt(2)

53. Mrfootballman97

so would it be sqrt(5) and 35= 7 * 5

54. Mrfootballman97

$\sqrt{5} \times \sqrt{7} \times \sqrt{5}$?

55. Mrfootballman97

but those are primes....

56. KonradZuse

yessir, but you can combine them in other ways, no?

57. KonradZuse

sqrt(5) * sqrt(5) = ?

58. Mrfootballman97

i dont know. So then what do i do?

59. Mrfootballman97

oh didnt see your comment

60. KonradZuse

Always remember when we have 2 of the same sqrt() we get the actual number

61. Mrfootballman97

25?

62. Mrfootballman97

oops 5

63. KonradZuse

sqrt(25)yes.

64. KonradZuse

and yes.

65. Mrfootballman97

wait...

66. KonradZuse

we now have our answer.

67. Mrfootballman97

so how do i write down this answer?

68. KonradZuse

5sqrt(7)

69. Mrfootballman97

ohhhh ok

70. KonradZuse

Math is awesome that you can combine and move things around to find whatever you need. Lets say we have sqrt(3) sqrt(3) and sqrt(4) the 2 sqrt(3) become a 3. and the sqrt(4) becomes a 2. Our answer is 6.

71. KonradZuse

But if we had lets say sq(15) and sqrt(3) we will have to split up the sqrt(15) into sqrt(3) sqrt(5) and then another sqrt(3) which we end up getting 3sqrt(5)

72. Mrfootballman97

ahhhhhhhh that makes sense! Are you a math teacher or something?

73. KonradZuse

haha na...

74. KonradZuse

I just know how much it sucks to not get proper help.....

75. Mrfootballman97

yeah man. Ok well you saved my grade! Thanks again

76. KonradZuse

No problem good luck ,anymore questions you can do @konradzuse to get me.

77. Mrfootballman97

ok lets hope i dont need to do that :P

78. KonradZuse

There are lots more math in your future :).

79. Mrfootballman97

true that.

80. KonradZuse

:) I just got done with Linear Algebra and Calculus 2 :)

81. Mrfootballman97

im half way through geometry...

82. Mrfootballman97

hey would the answer to sqrt of 9 over 5 = sqrt of 45 over 5?

83. Mrfootballman97

|dw:1358109390649:dw|

84. Mrfootballman97

@KonradZuse

85. KonradZuse

nope... what's sqrt(9)?

86. Mrfootballman97

3

87. Mrfootballman97

would it be:

88. Mrfootballman97

$\sqrt{3\sqrt{5}}$

89. KonradZuse

nope 3/sqrt(5)...

90. Mrfootballman97

ohh

91. Mrfootballman97

so just:

92. Mrfootballman97

|dw:1358110687298:dw|

93. Mrfootballman97

or should it have a sqrt sign over the entire thing?

94. KonradZuse

think about it. sqrt(9)/sqrt(5) is the same thing as sqrt(9/5) sqrt(9) is 3.

95. Mrfootballman97

ok thanks. Have a good day

96. KonradZuse

yup.

97. KonradZuse

you can also double check everything with a calculator...

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