SOLUTION: I submitted this question and got an answer but it's not one of the answer choices on my lesson sheet. I follow your explanation until step 5-6 then I don't understand the rest.

Algebra ->  Square-cubic-other-roots -> SOLUTION: I submitted this question and got an answer but it's not one of the answer choices on my lesson sheet. I follow your explanation until step 5-6 then I don't understand the rest.       Log On


   

Question 91108: I submitted this question and got an answer but it's not one of the answer choices on my lesson sheet. I follow your explanation until step 5-6 then I don't understand the rest. I am reposting the same question with the answer choices this time. I'm thinking the answer is "b" by the answer you came up with. Do you agree?
What is the square root of 162x^6 over 64x^2
The answer choices are: a. 3x^2 sq. root 2 over 8; b. 9x^2 sq. root 2 over 8
or c. 3x^2 sq. root 2 over 4 Thank you once again for your help.
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
162x%5E6%2F64x%5E2

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Lets simplify the numerator:


sqrt%28162%2Ax%5E6%29Start with the given expression
sqrt%2881%2A2%2Ax%5E6%29 Factor 162 into 81%2A2

sqrt%2881%2A2%2Ax%5E2%2Ax%5E2%2Ax%5E2%29 Factor x%5E6 into x%5E2%2Ax%5E2%2Ax%5E2

sqrt%2881%29%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

9%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29 Take the square root of the perfect square 81 to get 9

9%2Asqrt%282%29%2Ax%2Ax%2Ax Take the square root of the perfect squares x%5E2 to get x

9%2Asqrt%282%29%2Ax%5E3 Multiply the common terms
9%2Ax%5E3%2Asqrt%282%29 Rearrange the terms

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So the expression becomes

9%2Ax%5E3%2Asqrt%282%29%2F64x%5E2

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Lets simplify the denominator:

sqrt%2864%2Ax%5E2%29Start with the given expression

sqrt%2864%29%2Asqrt%28x%5E2%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

8%2Asqrt%28x%5E2%29 Take the square root of the perfect square 64 to get 8

8%2Ax Take the square root of the perfect square x%5E2 to get x

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So the expression becomes

9%2Ax%5E3%2Asqrt%282%29%2F8x


9%2Ax%5E%283-1%29%2Asqrt%282%29%2F8 Subtract the exponents

9%2Ax%5E2%2Asqrt%282%29%2F8 Simplify

So the answer is B). So you are correct.

Answer by Earlsdon(6294) About Me  (Show Source):