Question 1041243
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The answer is {{{8*sqrt(7)-7*root(3,x)}}}. Below I show how/why


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Notice how {{{sqrt(7)}}} comes up twice. So does {{{root(3,x)}}}. This suggests we'll be combining like terms. 



They are somewhat complicated expressions. Let's replace them temporarily. 



Let
{{{P=sqrt(7)}}}
{{{Q=root(3,x)}}}



we'll use those equations above to simplify



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{{{6*sqrt(7)-root(3,x)+2*sqrt(7)-6*root(3,x)}}}



{{{6*P-root(3,x)+2*P-6*root(3,x)}}} Replace EVERY copy of {{{sqrt(7)}}} with P



{{{6*P-Q+2*P-6*Q}}} Replace EVERY copy of {{{root(3,x)}}} with Q



After this point, we combine like terms. Just like how x+3x simplifies to 4



{{{6*P+2*P-Q-6*Q}}}



{{{(6*P+2*P)+(-Q-6*Q)}}} Group like terms



{{{(6+2)*P+(-1-6)*Q}}} Distributive property



{{{(8)*P+(-7)*Q}}} Simplify



{{{8*P-7*Q}}} Drop unneeded parenthesis



{{{8*sqrt(7)-7*Q}}} Replace P with {{{sqrt(7)}}}



{{{8*sqrt(7)-7*root(3,x)}}} Replace Q with {{{root(3,x)}}}



Side Note: {{{root(3,x)}}} is read as "cube root of x". It's similar, but not identical, to the square root. 


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So the final answer is {{{8*sqrt(7)-7*root(3,x)}}}
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