SOLUTION: I have been trying to do this problem for a while now, i tried doing it step by step and also checking it on the calculator but it gives me a different answer every time. 3squ

Algebra ->  Square-cubic-other-roots -> SOLUTION: I have been trying to do this problem for a while now, i tried doing it step by step and also checking it on the calculator but it gives me a different answer every time. 3squ      Log On


   

Question 95958: I have been trying to do this problem for a while now, i tried doing it step by step and also checking it on the calculator but it gives me a different answer every time.

3square root of 45 -2square root of 125
this is al together like side by side
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given to simplify:
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3%2Asqrt%2845%29-2%2Asqrt%28125%29
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On a calculator you can find that the square root of 45 is 6.708203932 so multiplying
the square root of 45 times 3 results in 3*6.708203932 = 20.1246118. Substituting this number
into the problem in place of 3%2Asqrt%2845%29 reduces the problem to:
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20.1246118+-+2%2Asqrt%28125%29
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Next you can use the calculator to find that sqrt%28125%29+=+11.18033989. Multiplying this
by -2 results in -2%2Asqrt%28125%29+=+-2%2A11.18033989+=+-22.36067977. Then substituting this
into the equation reduces the equation to:
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20.1246118+-+22.36067977+=+-2.236067975
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So the answer to this problem is -2.236067975 within the roundoff error on the last decimal
place.
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Now let's work the problem without doing it on a calculator. Start with:
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3%2Asqrt%2845%29-2%2Asqrt%28125%29
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Note that by the rules of radicals, sqrt%2845%29+=+sqrt%289%2A5%29+=+sqrt%289%29%2Asqrt%285%29+=+3%2Asqrt%285%29
So you can substitute 3%2Asqrt%285%29 for sqrt%2845%29 to get:
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3%2A3%2Asqrt%285%29+-+2%2Asqrt%28125%29
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Now let's simplify sqrt%28125%29:
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sqrt%28125%29+=+sqrt%2825%2A5%29+=+sqrt%2825%29%2Asqrt%285%29=+5%2Asqrt%285%29
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You can now substitute 5%2Asqrt%285%29 for sqrt%28125%29 to get:
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3%2A3%2Asqrt%285%29+-+2%2A5%2Asqrt%285%29
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Do the multiplications. 3*3 = 9 and -2*5 = -10. So this becomes:
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9%2Asqrt%285%29+-+10%2Asqrt%285%29
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You can factor sqrt%285%29 from each term to get:
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%289-10%29%2Asqrt%285%29
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Combine the two numbers in the parentheses to get:
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%28-1%29%2Asqrt%285%29+=+-1%2Asqrt%285%29+=+-sqrt%285%29
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So the answer we got is -sqrt%285%29. If you find the square root of 5 on a calculator
you will find that it is 2.236067977. Therefore, our answer becomes:
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-sqrt%285%29+=+-2.236067977
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This agrees with the answer we got by doing all the work on a calculator. So you can use
either method depending on what is compatible with the way your teacher wants it done.
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Hope this helps you to understand the problem and how to get the answer.
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