SOLUTION: ``Add or subtract terms whenever possible. 2 cubed root of 192 (192 is in square root) + cubed root of 24 (twenty four is in square root) Answer choices: A.) 10 cubed root 3

Algebra ->  Radicals -> SOLUTION: ``Add or subtract terms whenever possible. 2 cubed root of 192 (192 is in square root) + cubed root of 24 (twenty four is in square root) Answer choices: A.) 10 cubed root 3       Log On


   

Question 337678: ``Add or subtract terms whenever possible.
2 cubed root of 192 (192 is in square root) + cubed root of 24 (twenty four is in square root)
Answer choices:
A.) 10 cubed root 3
B.) 2 cubed root 216
C.) 4 cubed root 3
D.) 3 cubed root 216
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Another way of writting the cubed root is X^(-3)
So given: 2%2A%28192%29%5E-3+%2B+24%5E-3
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To remove numbers from under the radical, the number has to appear the number of times that the radical is raised to. For example sqrt%284%29+=+4%5E-2 Now the radical is raised to the second power so in order to remove a number from under the radical, the number must be there twice. Factor the 4. 4 = 2*2. Now rewrite the equation. 4%5E-2+=+2
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So for your given equation, we need to first find the factors of 24 and 192.
Lets start with 24
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24/3 = 8
8/2 = 4
6/2 = 2
So the factors of 24 = 2*2*2*3.
Notice that the 2 shows up three times.
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Find the factors of 192.
192/8 = 24
Now we just found the factors of 24 and 8
24 = 2*2*2*3
8 = 2*2*2
So the factors of 192 = 2*2*2*3*2*2*2
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Rewrite the given equation
2%2A%28192%29%5E-3+%2B+24%5E-3
2%2A%282%2A2%2A2%2A3%2A2%2A2%2A2%0D%0A%29%5E-3+%2B+%282%2A2%2A2%2A3%29%5E-3
Since both parts are raised to the -3 degree, we can take out a number as long as it shows up 3 times.
2%2A%282%2A2%29%2A3%5E-3+%2B+2%2A3%5E-3
Simplify
8%2A3%5E-3+%2B+2%2A3%5E-3
Simplify
10%2A3%5E-3