Problem Page The weight of 100 identical samples of a substance is 0.01 pound. What is the weight of 10 samples?
1 answer:
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Lets start by factoring the 216 into its smaller parts.
![\sqrt[3]{2 * 2 * 2 * 3 * 3 * 3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%20%2A%202%20%2A%202%20%2A%203%20%2A%203%20%2A%203%7D)
From here, we can separate the three 2s and the three 3s into two separate radicals.
![\sqrt[3]{2*2*2} * \sqrt[3]{3*3*3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%2A2%2A2%7D%20%2A%20%20%5Csqrt%5B3%5D%7B3%2A3%2A3%7D%20)
Since we have three copies of the same number in each, the answer to the cube root is the number we have the copies of.
![\sqrt[3]{2*2*2} * \sqrt[3]{3*3*3} = 2 * 3](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B2%2A2%2A2%7D%20%2A%20%20%5Csqrt%5B3%5D%7B3%2A3%2A3%7D%20%3D%202%20%2A%203)
Finally, we just need to multiply out what remains to find the solution.
So, the final answer is 6.
From here, we can separate the three 2s and the three 3s into two separate radicals.
Since we have three copies of the same number in each, the answer to the cube root is the number we have the copies of.
Finally, we just need to multiply out what remains to find the solution.
So, the final answer is 6.