course Mth 158 ??~??????????assignment #008008. `query 8
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13:58:15 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 --> The only thing we can do is to find the sqrt of 4 which is 2. This problem in simplified form is 2* sqrt (x + 4)^2 confidence assessment: 1
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14:01:11 ** 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 --> I din't split the question into two separate parts. I understand how to do that know. I was right about the sqrt of 4 = 2, but I didn't find the sqrt of (x + 4)^2. I see where I went wrong. self critique assessment: 2
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14:04:18 Extra Question: What is the simplified form of (24)^(1/3) and how did you get this result?
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RESPONSE --> I know that when a fraction is used as an exponent, the numerator is the power to which it is raised, and the denominator is the root. In this case, the numerator is 1 so 24^1 = 24. Since the denominator is 3 you would take the cube root. The simplified form is cube root (24) confidence assessment: 1
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14:05:51 ** (24)^(1/3) = (8 * 3)^(1/3) = 8^(1/3) * 3^(1/3) = 2 * 3^(1/3) **
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RESPONSE --> I see my mistake I should've split 24 into 8*3. I understand my mistake and how to get the correct answer. self critique assessment: 2
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14:17:45 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^2 y)^1/3 = x^2/3 y^3 (125x^3)^1/3 = 125x (8x^3 y^4)^1/3 = 2x y^4/3 125x* x^2/3 y^3 = (125 x^5/3 y^3) / (2x y^4/3). When you divide exponents, you must subtract the numerator from the denominator. (125x^2/3 y^5/3) / 2 confidence assessment: 1
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14:24:05 ** (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 --> I got that one completely wrong. I cubed 125 then took the cube root when I should've just taken the cube root. I'm not sure why you didn't multiply 4*1/3 in the last part of the problem to get y^4/3. self critique assessment: 2
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14:28:02 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 --> First you can split 12 into sqrt 4 * sqrt 3. The sqrt of 4 is 2. You can also split 27 into sqrt 9 * sqrt of 3. That gives you 2(2) * sqrt 3 - 3(3) * sqrt 3. 4*sqrt 3 - 9*sqrt 3 confidence assessment: 2
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14:29:15 ** 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 --> I forgot the last step, I wasn't sure if I could combine the like radical, I see now that I should have. self critique assessment: 2
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14:31:42 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 --> (2 sqrt(6) + 3) (3 sqrt(6)) 3 + 5sqrt(6) confidence assessment: 1
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14:34:30 ** (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 --> I didn't use that distributive law, but I understand that I should have. I understand how to multiply everything out and how you got your answer. self critique assessment: 2
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14:35:46 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 get rid of the radical in the denominator, you must multiply the whole fraction by the radical. 5(sqrt 10) / sqrt10 *sqrt 10. 5 sqrt 10 / 10 confidence assessment: 2
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14:36:29 ** 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 --> I didn't simplify 5/ 10, thats where I messed up. self critique assessment: 2
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14:43:46 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 --> I multiplied the whole fraction by (4 + sqrt(2). 10 (4 + sqrt(2) / (4 - sqrt(2) * (4 + sqrt(2). 40 + 10sqrt(2)/ 16 - 2 40 + 10sqrt(2) / 14 then I simplified to get (20 + 5sqrt(2)) / 7 confidence assessment: 2
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14:44:04 ** 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 --> Thats what I did. self critique assessment: 3
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14:45:04 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I realized I didn't know as much about radicals as I thought. I've forgotten some of the rules I have learned, but I'm sure they will come back to me. confidence assessment: 3
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