Question

a builder needs three pipes of different lengths. the pipes are $6\sqrt{96}$ feet long, $12\sqrt{150}$ feet long, and $2\sqrt{294}$ feet long. how many feet of piping is required in all? (hint: try dividing each radicand by 6.) options: $20\sqrt{6}$ feet, $98\sqrt{6}$ feet, $20\sqrt{294}$ feet, $20\sqrt{540}$ feet

Explanation:

Step1: Simplify $6\sqrt{96}$

Factor 96 into $16 \times 6$:
$6\sqrt{96} = 6\sqrt{16 \times 6} = 6 \times 4\sqrt{6} = 24\sqrt{6}$

Step2: Simplify $12\sqrt{150}$

Factor 150 into $25 \times 6$:
$12\sqrt{150} = 12\sqrt{25 \times 6} = 12 \times 5\sqrt{6} = 60\sqrt{6}$

Step3: Simplify $2\sqrt{294}$

Factor 294 into $49 \times 6$:
$2\sqrt{294} = 2\sqrt{49 \times 6} = 2 \times 7\sqrt{6} = 14\sqrt{6}$

Step4: Sum the simplified terms

Add the like radicals:
$24\sqrt{6} + 60\sqrt{6} + 14\sqrt{6} = (24+60+14)\sqrt{6} = 98\sqrt{6}$

Answer:

98√6 feet