how do I simplify cube roots?

Question

anonymous · Answer

i understand some of it but when it comes down to the prime part i lose it sorta

psymon · Answer

Well, let's say we have something like this:
$$\sqrt[3]{375y ^{5}} $$
Now it helps to know some common cube roots. Mainly 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125, 6^3 = 216. So what helps is to know that we can factor what is inside of the cube root and turn it into a bunch of multiples. This is what I mean:
$$\sqrt[3]{375y ^{5}}=\sqrt[3]{375}*\sqrt[3]{y ^{3}}*\sqrt[3]{y ^{2}}$$If you can factor the inside, you can break it up into as many multiplications as you want. Does that kind of make sense?

anonymous · Answer

yes ok so here is what i have a problem with $$\sqrt[3]{98} * \sqrt[3]{7} $$ then she wants us to do $$\sqrt[3]{98*7}$$ then under it to multiply and stuff

psymon · Answer

Correct. That is perfectly fine to do. You can multiply any sort of factors of what you have as long as they are the same root.

anonymous · Answer

Okay so i get that part but then under it i write 7 * 98 then circle the seven because it is prime and then under then 98 i do 7 * 14 and then again circle the 7 but then i get to 14 and do 7 times 2 and circle the 7 and 2 but what is my answer? and how do i find it

psymon · Answer

Well, we have to see if it is at all possible to find one of our cube roots inside of what we got. So that is why we need to know 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125, 6^6 = 216. Usually I dont go much further than that. So the first thing we could do is see if any of those cube roots divide equally into 98. If they do not, then I would try to multiply 08 and 7 and then try to divide.

anonymous · Answer

Okay So i am still confused a little could you maybe draw it out

anonymous · Answer

?

psymon · Answer

Yeah, sure. 
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