Question

a plumber 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?
a. $98\sqrt{6}$ feet
b. $20\sqrt{540}$ feet
c. $20\sqrt{294}$ feet
d. $20\sqrt{6}$ feet

Explanation:

Step1: Simplify \(6\sqrt{96}\)

Factor 96: \(96 = 16\times6\), so \(\sqrt{96}=\sqrt{16\times6}=4\sqrt{6}\). Then \(6\sqrt{96}=6\times4\sqrt{6}=24\sqrt{6}\).

Step2: Simplify \(12\sqrt{150}\)

Factor 150: \(150 = 25\times6\), so \(\sqrt{150}=\sqrt{25\times6}=5\sqrt{6}\). Then \(12\sqrt{150}=12\times5\sqrt{6}=60\sqrt{6}\).

Step3: Simplify \(2\sqrt{294}\)

Factor 294: \(294 = 49\times6\), so \(\sqrt{294}=\sqrt{49\times6}=7\sqrt{6}\). Then \(2\sqrt{294}=2\times7\sqrt{6}=14\sqrt{6}\).

Step4: Sum the simplified radicals

Add \(24\sqrt{6}+60\sqrt{6}+14\sqrt{6}\). Combine like terms: \((24 + 60 + 14)\sqrt{6}=98\sqrt{6}\).

Answer:

A. \(98\sqrt{6}\) feet