course Mth 158 nK{ިzFassignment #008
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13:38:37 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 --> confidence assessment: 0
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13:43:47 ** (24)^(1/3) = (8 * 3)^(1/3) = 8^(1/3) * 3^(1/3) = 2 * 3^(1/3) **
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RESPONSE --> ok self critique assessment: 2.
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13:50:50 ** (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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RESPONSE --> ok self critique assessment: 2
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13:51:45 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 --> ok confidence assessment: 0
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13:53:17 ** 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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RESPONSE --> ok self critique assessment: 2
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13:54:05 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 --> ok confidence assessment: 0
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13:56:28 ** (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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RESPONSE --> ok self critique assessment: 2
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FȂKT{mw assignment #008 008. `query 8 College Algebra 02-06-2007
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14:05:48 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 --> sqrt(4(x+4)^2)= =sqrt(4) * sqrt(x+4)^2 =2 * |x+4| confidence assessment: 2
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14:06:09 ** 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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RESPONSE --> Okay! I finally understand. self critique assessment: 2
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14:10:37 Extra Question: What is the simplified form of (24)^(1/3) and how did you get this result?
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RESPONSE --> (24)^(1/3)= = [ (8) (3) ] (1/3) = (8)^(1/3) * (3)^(1/3) = 2 * 3^(1/3) confidence assessment: 2
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14:10:44 ** (24)^(1/3) = (8 * 3)^(1/3) = 8^(1/3) * 3^(1/3) = 2 * 3^(1/3) **
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RESPONSE --> self critique assessment: 2
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14:25:35 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 --> (x^2y)^(1/3) * (125x^3)^(1/3) / (8x^3y^4)(1/3) = = (x^2)^(1/3) * y^(1/3) * (125)^(1/3)(x^3)^(1/3) / 8^(1/3) * (x^3)^(1/3) * (y^3)^(1/3) * y^(1/3) =x^(2/3) * y^(1/3) * 5x / 2xy * y^(1/3) =5x^(3/3) * x^(2/3) / 2xy =5x^(2/3) / 2y confidence assessment: 2
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14:25:53 ** (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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RESPONSE --> Ok self critique assessment: 2
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14:31:26 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) - 3sqrt(27)= Find like radicals for combinding 2sqrt(4*3) - 3sqrt(9*7) or 2sqrt(4) * sqrt(3) - 3sqrt(9) * sqrt(3)= 2 * 2 * sqrt(3) - 3 * 3 * sqrt(3)= 4sqrt(3) - 9sqrt(3)= -5sqrt(3) confidence assessment: 2
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14:31:40 ** 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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RESPONSE --> Yes! self critique assessment: 2
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14:38:04 ** (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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RESPONSE --> Okay, to be understood by using the distributive law. (3 * sqrt(6)) to be multiplied by both (2 * sqrt(6)) and 3 (3 * sqrt(6)) * (2 * sqrt(6)) + (3 * sqrt(6)) * (3) = (3*2)(sqrt(6) * sqrt(6)) + (3*3) * sqrt(6) = (6 * 6) + 9sqrt(6)= 36 + 9sqrt(6) self critique assessment: 2
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14:42:07 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 --> To rationalize the denominator of 5/sqrt(10), it is that both the denominator and numerator to be multiplied by sqrt(10). 5/sqrt(10) * sqrt(10)/sqrt(10)= 5sqrt(10)/(sqrt(10))^2= 5sqrt(10)/10+ sqrt(10)/2 confidence assessment: 2
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14:42:40 ** 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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RESPONSE --> whoooah! ok I am really getting this... self critique assessment: 2
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14:48:23 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 --> To rationalize the denominator of 10/(4-sqrt(2)), it is to be multiplied by both the numerator and denominator by (4+sqrt(2)). 10(4+sqrt(2)) / (4)^2 - (sqrt2)^2= 40+10sqrt(2) / 16-2= 40+10sqrt(2) / 14 confidence assessment: 2
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14:49:46 ** 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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RESPONSE --> Okay so it was to be simplified once more by 2 giving (20 + 5sqrt(2)) / 7 self critique assessment: 2
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14:50:45 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> At first I had a hard time understanding, but finally got the biggests part of what I was missing. confidence assessment: 3
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