SOLUTION: 13 sqrt 20 - 15 sqrt 32 - 8 sqrt 45 + 7 sqrt 8

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Question 199837: 13 sqrt 20 - 15 sqrt 32 - 8 sqrt 45 + 7 sqrt 8
Found 2 solutions by RAY100, jim_thompson5910:
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
13 sqrt20 -15 sqrt32 -8sqrt45+7sqrt8
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factor all radicals for largest perfect square
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13 sqrt( 4*5) -15 sqrt(16*2) -8sqrt(9*5) +7sqrt(4*2)
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13 sqrt4 * sqrt5 - 15 sqrt16 *sqrt2 -8sqrt9*sqrt5 +7 sqrt4*sqrt2
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13*2sqrt5 -15*4sqrt2 -8*3sqrt5 +7*2sqrt2
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collect like terms
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26 sqrt5 -24sqrt5 -60sqrt2 +14 sqrt2
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2 sqrt5 -46 sqrt2
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check using calculator on original and answer,,,,both = -60.58,,,,,ok

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
13%2Asqrt%2820%29-15%2Asqrt%2832%29-8%2Asqrt%2845%29%2B7%2Asqrt%288%29 Start with the given expression


13%2A2%2Asqrt%285%29-15%2Asqrt%2832%29-8%2Asqrt%2845%29%2B7%2Asqrt%288%29 Simplify sqrt%2820%29 to get 2%2Asqrt%285%29.


13%2A2%2Asqrt%285%29-15%2A4%2Asqrt%282%29-8%2Asqrt%2845%29%2B7%2Asqrt%288%29 Simplify sqrt%2832%29 to get 4%2Asqrt%282%29.


13%2A2%2Asqrt%285%29-15%2A4%2Asqrt%282%29-8%2A3%2Asqrt%285%29%2B7%2Asqrt%288%29 Simplify sqrt%2845%29 to get 3%2Asqrt%285%29.


13%2A2%2Asqrt%285%29-15%2A4%2Asqrt%282%29-8%2A3%2Asqrt%285%29%2B7%2A2%2Asqrt%282%29 Simplify sqrt%288%29 to get 2%2Asqrt%282%29.


26%2Asqrt%285%29-15%2A4%2Asqrt%282%29-8%2A3%2Asqrt%285%29%2B7%2A2%2Asqrt%282%29 Multiply 13 and 2 to get 26.


26%2Asqrt%285%29-60%2Asqrt%282%29-8%2A3%2Asqrt%285%29%2B7%2A2%2Asqrt%282%29 Multiply 15 and 4 to get 60.


26%2Asqrt%285%29-60%2Asqrt%282%29-24%2Asqrt%285%29%2B7%2A2%2Asqrt%282%29 Multiply 8 and 3 to get 24.


26%2Asqrt%285%29-60%2Asqrt%282%29-24%2Asqrt%285%29%2B14%2Asqrt%282%29 Multiply 7 and 2 to get 14.


2%2Asqrt%285%29-46%2Asqrt%282%29 Combine like terms.



So 13%2Asqrt%2820%29-15%2Asqrt%2832%29-8%2Asqrt%2845%29%2B7%2Asqrt%288%29 simplifies to 2%2Asqrt%285%29-46%2Asqrt%282%29.



In other words, 13%2Asqrt%2820%29-15%2Asqrt%2832%29-8%2Asqrt%2845%29%2B7%2Asqrt%288%29=2%2Asqrt%285%29-46%2Asqrt%282%29