Question

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?

Answer 1

80 feet How many feet of piping is required in all? (Hint: Try dividing each radicand by 6.)

Answer 2

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