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A plumber is fitting pipes for a remodeled kitchen sink. The sink requires 3 different sections of pipe; the first is 6√96 feet long, the second section is 12√150 feet long, and the third section is 2√294 feet long. How many feet of piping is required for all 3 sections?

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98 √6 feet is required for all 3 sections.

6 √96 + 12 √150 + 2 √294  = 0

Simplify each radical to be the same.

   6 √96  =   6 √16 * 6 =   6 * 4 √6 = 24 √6
12 √150 = 12 √25 * 6 = 12 * 5 √6 = 60 √6 
  2 √294 =   2 √49 * 6 =   2 * 7 √6 = 14 √6

Add the radicals.

24 √6 + 60 √6 + 14 √6 = 98 √6 feet

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