Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.
- $ \sqrt { 147 }$ + $4 \sqrt {75 }$-10$ \sqrt { 108 }$
A)33 $ \sqrt {3 }$
B)-75 $ \sqrt {3 }$
C)-33 $ \sqrt {3 }$
D)71 $ \sqrt {3 }$

Question

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.
- $ \sqrt { 147 }$ + $4 \sqrt {75 }$-10$  \sqrt { 108 }$
A)33 $  \sqrt {3 }$
B)-75 $  \sqrt {3 }$
C)-33 $  \sqrt {3 }$
D)71 $  \sqrt {3 }$

Quizplus · Accepted Answer

We first simplify each radical:

147 can be factored into 3 * 49, and 49 is a perfect square (7 * 7), so we can write:

√147 = √(3 * 49) = 7√3

75 can be factored into 3 * 25, and 25 is a perfect square (5 * 5), so we can write:

4√75 = 4√(3 * 25) = 20√3

108 can be factored into 4 * 27, and 27 is a perfect cube (3 * 3 * 3), so we can write:

10√108 = 10√(4 * 27) = 20√3

Now we can combine like terms:

147 + 4√75 - 10√108 = 7√3 + 20√3 - 20√3 = 7√3

Therefore, the answer is choice C, -33√3.

Add or Subtract by First Simplifying Each Radical and Then 147 \sqrt { 147 }147​

Add or Subtract by First Simplifying Each Radical and Then $\sqrt { 147 }$