To simplify the expressions provided and see which one equals \( 87 - \sqrt{3} \), let's evaluate each option.
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\( 256 - \sqrt{3} - 47 - \sqrt{3} \): \[ 256 - 47 - \sqrt{3} - \sqrt{3} = 256 - 47 - 2\sqrt{3} = 209 - 2\sqrt{3} \]
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\( 2 \sqrt[3]{56} - 4 \sqrt[3]{7} \): Since this doesn't seem to involve any addition or subtraction of square roots or simply can be evaluated to give a numerical value, we will leave it for now.
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\( 56 - \sqrt{3} + 67 - \sqrt{3} \): \[ 56 - \sqrt{3} + 67 - \sqrt{3} = (56 + 67) - (1 + 1)\sqrt{3} = 123 - 2\sqrt{3} \]
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\( \sqrt[3]{56} + 6 \sqrt[3]{7} \): As with the previous cube root expression, direct evaluation or further simplification isn't straightforward without numerical estimates, so we leave this as well.
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\( -6 \sqrt[3]{7} - 2 \sqrt[3]{7} \): \[ -6 \sqrt[3]{7} - 2 \sqrt[3]{7} = -8 \sqrt[3]{7} \]
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\( 36 - \sqrt{3} + 51 - \sqrt{3} \): \[ 36 - \sqrt{3} + 51 - \sqrt{3} = (36 + 51) - (1 + 1)\sqrt{3} = 87 - 2\sqrt{3} \]
None of the directly simplified combinations yield \( 87 - \sqrt{3} \), but we know that \( 87 - \sqrt{3} \) can be derived from \( 87 - 2\sqrt{3} \) if we took \(- \sqrt{3}\) and retained \(87\).
Given this systematic approach, based on the options presented, it appears that none of the expressions directly simplify to \( 87 - \sqrt{3} \) as per the calculations shown. The closest simplified form we derived was \( 87 - 2\sqrt{3} \) from the fifth option.
Please double-check the expressions in the original query for potential adjustments or any miscommunication, as none of these fully match the original target expression without further manipulation.
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