Question

A builder needs three pipes of different lengths. The pipes are feet long, feet long, and feet long. How many feet of piping is required in all? (Hint: Try dividing each radicand by 6.)

Answer 1

Answer:

$98\sqrt{6}\ ft$

Step-by-step explanation:

The complete question is

A builder needs three pipes of different lengths. The pipes are 6√96 feet long, 12√150 feet long, and 2√294 feet long. How many feet of piping is required in all?

we know that

$6\sqrt{96}\ ft=6\sqrt{16(6)} =6\sqrt{4^{2}(6)}=6(4)\sqrt{6} =24\sqrt{6}\ ft$

$12\sqrt{150}\ ft=12\sqrt{25(6)} =12\sqrt{5^{2}(6)}=12(5)\sqrt{6} =60\sqrt{6}\ ft$

$2\sqrt{294}\ ft=2\sqrt{49(6)} =2\sqrt{7^{2}(6)}=2(7)\sqrt{6} =14\sqrt{6}\ ft$

Sum the length of the three pipes

$24\sqrt{6}+60\sqrt{6}+14\sqrt{6}=98\sqrt{6}\ ft$