how do you solve this radical problem

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how do you solve this radical problem

Mathematics
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|dw:1441681695839:dw|
in thorough steps cuz i don't seem to understand this
So you will need to simplify each radical and then multiply them together. Let's start with the first one. We know that 2^3 is 8 and 3^3 is 27, so it only follows that the cube root of 15 must be in between 2 and 3 as 15 is between 8 and 27 and the opposite of an exponent is a root. But where is it between 2 and 3? Well, to figure that out we must approximate. But that is a very long process. So instead, let's go through the first-decimal-digit possibilities. Let's start with ones closer to 2 as 8 is closer to 15. \[2.2^{3}=10.648\] Not quite. \[2.4^{3}=13.824\] Closer... let's try one more. \[2.5^{3}=15.625\] That's a bit too far. So we know it must be a bit smaller than 2.5 but quite a bit bigger than 2.4 You could keep repeating this process until you get it perfect, but I quite honestly do not feel like it. So I plugged it into my calculator and get approximately 2.466 Now for the next one. Cube root of 75. Well, 8^3=64 and 9^3=81, so it must be between 8 and 9. You could repeat the process above, but the calculator informs me it is about 4.217 Now for the easy part! \[2.466\times4.217=10.399\]

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but its still supposed to be in radical form not decimal
Ah... that's different.
can you explain in that way?
I shall try =)
Find the prime factorization of both numbers |dw:1441682872453:dw|
You're taking a cube root, so look for group of 3 numbers|dw:1441683029075:dw|
Going off of what peachpi said, then you can multiply those under the cube root\[\sqrt[3]{5\times3\times5\times5\times3}\] and then see that there are 3 5's. Because it is a cube root, only one 5 can stay, and we pull it out of the cube root, so we are left with \[5\sqrt[3]{3\times3}\]
Write the grouped number on the outside of the radical, multiply the numbers left in the radical|dw:1441683084511:dw|
There you go!!
doesn't the rad 9 come out of the square root
No. Because it is a cube root and not a square root. 2^3 is only 8, while 3^3 is 27. This is the simplest you will be able to get in radical form =)
okay can i ask for your help for one more problem
Sure =)
|dw:1441683413491:dw|
You'll need to do something similar here, but I have not learned how to find roots of fractions yet. I could do it in decimal form, but I know that's not what you need. I'm very sorry!!
it's fine thanks for your help!
No problem =)

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