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).
A.
20sqrt(6)
B.
98sqrt(6) feet
C.
20sqrt(94) feet
D.
20sqrt(540) feet

*question has been edited by a moderator to provide more information*

Answer 1

"how many feet of piping is required for all three sections" implies we should add the lengths of the pipes

12sqrt(150) + 6sqrt(96) + 2sqrt(294)

these are not like radicals but we can turn them by dividing each radicand by 6 as the problem suggests

12sqrt(150/6) + 6sqrt(96/6) + 2sqrt(294/6)

of course, to preserve the values of the problem, we must also multiply each term by sqrt(6)

12sqrt(150/6)*sqrt(6) + 6sqrt(96/6)*sqrt(6) + 2sqrt(294/6)*sqrt(6)

from there, simply simplify the division within the radicals (leaving the sqrt(6) part alone). then combine the terms at the end.