Assignment 8

course MTH 158

I am really having difficulty with this.

assignment #008008. `query 8

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College Algebra

09-19-2007

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18:33:27

R.8.64. What is the simplified form of sqrt( 4 ( x+4)^2 ) and how did you get this result?

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RESPONSE -->

First start by squaring the entire problem

[sqrt( 4 ( x+4)^2)]^2

leaving 4 (x+4)^4

simplifying:

4 (x^4 +16)

4x^4 +16

confidence assessment: 0

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18:33:38

09-19-2007 18:33:38

** sqrt(a b) = sqrt(a) * sqrt(b) and sqrt(x^2) = | x | (e.g., sqrt( 5^2 ) = sqrt(25) = 5; sqrt( (-5)^2 ) = sqrt(25) = 5. In the former case x = 5 so the result is x but in the latter x = -5 and the result is | x | ).

Using these ideas we get

sqrt( 4 ( x+4)^2 ) = sqrt(4) * sqrt( (x+4)^2 ) = 2 * | x+4 | **

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NOTES ------->

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Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the given solution, and if necessary asking specific questions (to which I will respond).

&#

Note that sqrt(z) means 'the square root of z'. You appear to be treating it as the square of z.

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18:36:21

Extra Question: What is the simplified form of (24)^(1/3) and how did you get this result?

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RESPONSE -->

Simplified it is

^3sqrt(24)

being 2.88

confidence assessment: 0

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18:36:33

09-19-2007 18:36:33

** (24)^(1/3) =

(8 * 3)^(1/3) =

8^(1/3) * 3^(1/3) =

2 * 3^(1/3) **

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NOTES ------->

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18:39:14

Extra Question:. What is the simplified form of (x^2 y)^(1/3) * (125 x^3)^(1/3) / ( 8 x^3 y^4)^(1/3) and how did you get this result?

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RESPONSE -->

I do not know

confidence assessment: 09

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18:39:18

09-19-2007 18:39:18

** (x^2y)^(1/3) * (125x^3)^(1/3)/ ( 8 x^3y^4)^(1/3)

(x^(2/3)y^(1/3)* (5x)/[ 8^(1/3) * xy(y^(1/3)]

(x^(2/3)(5x) / ( 2 xy)

5( x^(5/3)) / ( 2 xy)

5x(x^(2/3)) / ( 2 xy)

5 ( x^(2/3) ) / (2 y) **

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NOTES ------->

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18:44:14

Extra Question:. What is the simplified form of 2 sqrt(12) - 3 sqrt(27) and how did you get this result?

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RESPONSE -->

2sqrt(12)= 2sqrt (4*3) = 2 * 4 sqrt(3)

should be 2 * sqrt(4) sqrt(3), not 2 * 4 sqrt(3).

-3sqrt(27)=-3sqrt(9*3)= -3*9 sqrt(3)

8 sqrt (3) -27 sqrt (3)

-19sqrt(3)

confidence assessment: 2

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18:44:23

09-19-2007 18:44:23

** 2* sqrt(12) - 3*sqrt(27) can be written as

2* sqrt (4*3) - 3 * sqrt (9*3) by factoring out the maximum possible perfect square in each square root. This simplifies to

2* sqrt (4) sqrt(3) - 3 * sqrt (9) sqrt(3) =

2*2 sqrt 3 - 3*3 * sqrt 3 =

}

4*sqrt3 - 9 * sqrt3 =

-5sqrt3. **

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NOTES ------->

&#

This also requires a self-critique.

&#

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18:47:13

R.8.78. What is the simplified form of (2 sqrt(6) + 3) ( 3 sqrt(6)) and how did you get this result?

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RESPONSE -->

2sqrt(9) * 3sqrt(6)

order of operations: 2 sqrt(6) + 3 requires that you do sqrt(6), then multiply that by 2, before adding 3.

To get 2 sqrt(9) the expression would have to be 2 sqrt(6+3), which is very different.

the square of 9 is 3, and the cube of 6 is 2

3 * 2

6

confidence assessment: 2

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18:47:19

09-19-2007 18:47:19

** (2*sqrt(6) +3)(3*sqrt(6)) expands by the Distributive Law to give

(2*sqrt(6) * 3sqrt(6) + 3*3sqrt(6)), which we rewrite as

(2*3)(sqrt6*sqrt6) + 9 sqrt(6) =

(6*6) + 9sqrt(6) =

36 +9sqrt(6). **

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NOTES ------->

&#

You need a detailed self-critique here.

&#

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18:50:33

R.8.90. What do you get when you rationalize the denominator of 5 / sqrt(10) and what steps did you follow to get this result?

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RESPONSE -->

start by multiplying the num and denom by sqrt(10)

5sqrt(10) / sqrt(10)

square the denom

5sqrt(10)/100

sqrt(10)*sqrt(10) = sqrt(100) = 10

confidence assessment: 0

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18:50:39

09-19-2007 18:50:39

** Starting with 5/sqrt10 we multiply numerator and denominator by sqrt(10) to get

(5*sqrt10)/(sqrt10*sqrt10) =

(5sqrt10)/10 =

sqrt10/2 **

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NOTES ------->

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18:52:46

R.8.96. What do you get when you rationalize the denominator of 10 / (4 - sqrt(2) ) and what steps did you follow to get this result?

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RESPONSE -->

multiply num and denom by sqrt(2)

10sqrt(2)/[4(sqrt(2)]^2

order of operations: 4 - sqrt(2) is very different than 4 sqrt(2), and in any case the 4 won't end up being squared.

10sqrt2/(4*2)

10sqrt(2)/8

confidence assessment: 3

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18:52:55

09-19-2007 18:52:55

** Starting with

10/(4-sqrt2) multiply both numerator and denominator by 4 + sqrt(2) to get

(10* (4+sqrt2))/ (4-sqrt2)(4+sqrt2). Since (a-b)(a+b) = a^2 - b^2 the denominator is (4+sqrt(2) ) ( 4 - sqrt(2) ) = 16 - 2 = 14 so we have

(40+ 10sqrt2) / 14. Dividing numerator and denominator by 2 we end up with

(20 + 5 sqrt(2) / 7 **

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NOTES ------->

&#

Self-critique should be included here.

&#

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18:53:19

Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

Absolutely none of this made since. I am truly lost right now...........................................

confidence assessment: 3

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18:53:27

Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

ok

confidence assessment: 3

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I've inserted some comments, but the main thing you need to do is dig into the given solutions and insert self-critiques so I'll have a clearer idea what you do and do not understand.

You understand the basics in Section 7.

In Section 8 you are having more trouble, but if you do the self-critique I we can get you straight without undue difficulty.

Useful resource on rationalizing denominators: http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut41_rationalize.htm

That page is a subpage of what appears to be a pretty good source for intermediate algebra review. The source is at

http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/index.htm

and you might want to look over Tutorials 37 - 41.