Answer:
98√6 feet
Step-by-step explanation:
To add these, we must first simplify each radical. We do this by finding the prime factorization of each number under the radical:
6√(96) = 6√(12*8) = 6√(2*6*2*4) = 6√(2*2*3*2*2*2)
We want to take out pairs; there are two pairs of twos, so we take two 2's out:
2*2*6√(2*3) = 24√6
For the second radical,
12√(150) = 12√(10*15) = 12√(5*2*5*3)
There is one pair of 5s, so we take one 5 out:
12*5√(2*3) = 60√6
For the third radical,
2√(294) = 2√(2*147) = 2√(2*3*49) = 2√(2*3*7*7)
There is a pair of 7s, so we take one 7 out:
7*2√(2*3) = 14√6
We now add:
24√6 + 60√6 + 14√6 = 84√6 + 14√6 = 98√6
The total length of the pipes is required.
The length of the piping is [tex]98\sqrt{6}\ \text{feet}[/tex]
The length of the pipes are
[tex]6\sqrt{96}=6\sqrt{2\times 2\times2\times2\times2\times3}=6\times 4\sqrt{6}=24\sqrt{6}[/tex]
[tex]12\sqrt{150}=12\sqrt{5\times 5\times 6}=12\times5\sqrt{6}=60\sqrt{6}[/tex]
[tex]2\sqrt{294}=2\sqrt{7\times 7\times 6}=2\times7\sqrt{6}=14\sqrt{6}[/tex]
Since, all the root terms are equal they can be added.
[tex]24\sqrt{6}+60\sqrt{6}+14\sqrt{6}=98\sqrt{6}[/tex]
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