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Mathematics 16 Online
OpenStudy (anonymous):

Which expression is equivalent to equation?

OpenStudy (anonymous):

\[\sqrt[3]{27n^5m^3p^2}\]

OpenStudy (freckles):

isn't 27=3*3*3 what is the cube root of 27?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

the square root is 5.19615242271

OpenStudy (freckles):

square root doesn't equal cube root

OpenStudy (anonymous):

i could post the answers if it will help .

OpenStudy (freckles):

we are doing cube root here because there is a 3 on the outside

OpenStudy (anonymous):

well the cube root is 3

OpenStudy (freckles):

right so we can do the same thing for the other variables... we know \[n^5=n^3n^2 \\ \text{ and } n^3=n \cdot n \cdot n \text{ so the cube root of } n^3 is ?\]

OpenStudy (anonymous):

I honestly have no clue ?

OpenStudy (freckles):

i will give you a hint 27 is a perfect cube that is 27 can be written as 3^3 and you said the cube root of 3^3 is 3 so the cube root of n^3 is ?

OpenStudy (anonymous):

3 ?

OpenStudy (freckles):

hmm n^3 is a variable so the cube root of n^3 should be a variable

OpenStudy (freckles):

\[\sqrt[3]{x^3}=x\]

OpenStudy (anonymous):

dang .

OpenStudy (freckles):

\[\sqrt[3]{27} \sqrt[3]{n^3} \sqrt[3]{m^3} \sqrt[3]{n^2 p^2} \\ \text{ you said } \sqrt[3]{27}=3 \\ \text{ so we have so far } \\ 3 \sqrt[3]{n^3} \sqrt[3]{m^3} \sqrt[3]{n^2 p^2}\]

OpenStudy (freckles):

so see if you can finish simplifying this using the fact that cube root of x^3 is x

OpenStudy (anonymous):

\[3nm \sqrt[3]{}n^2p^2 \]

OpenStudy (freckles):

yes because the cube root of n^3 is n and the cube root of m^3 is m and i believe you have written \[3nm \sqrt[3]{n^2p^2}\] which is good

OpenStudy (anonymous):

Yea my bad is that it ?? because that isnt one of the choices ,

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