Question

A plumber is fitting pipes for a remodeled kitchen sink. The sink requires 3 different sections of pipe; the first is 6sqrt(96) feet long, the second section is 12sqrt(150) feet long, and the third section is 2sqrt(294) feet long. How many feet of piping is required for all 3 sections? (Hint: Try dividing each radicand by 6).

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Answer 1

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Answer 2

like the hint says let's try dividing each radicand by 6. in order to keep the values the same we will also multiply each term by sqrt(6)

6sqrt(96) feet long, the second section is 12sqrt(150) feet long, and the third section is 2sqrt(294) feet long.

6sqrt(96) ---> 6sqrt(16)*sqrt(6)
12sqrt(150) ---> 12sqrt(25)*sqrt(6)
2sqrt(294) ---> 2sqrt(49)*sqrt(6)

now, sqrt(6) can't be simplified further since 6 is not a perfect square. however, 16, 25, and 49 ***are*** perfect squares. so you can simply re-write sqrt(16), sqrt(25), and sqrt(49) as their respective integers and simplify the products. (remember to leave sqrt(6) alone)

the result will be three terms all written in terms of sqrt(6). after that it's just simple addition.