Question

simplify the expression then add
its the very first part I am not getting how to simplify it
\[\sqrt[3]{54m^4}+m \sqrt[3]{16m} \]

Answer 1

Hi satellite73

Answer 2

first of all
\[54=27\times 2\] so
\[\sqrt[3]{54}=\sqrt[3]{27\times 2}=\sqrt[3]{27}\times \sqrt[3]{2}=3\sqrt[3]{2}\]

Answer 3

hi
so we can start to rewrite the first term

Answer 4

also
\[\sqrt[3]{m^4}=\sqrt[3]{m^3\times m}=\sqrt[3]{m^3}\times \sqrt[3]{m}=m\sqrt[3]{m}\]

Answer 5

putting these together we get
\[\sqrt[3]{54m^4}=3m\sqrt[3]{2m}\]

Answer 6

for the second term, \(16=8\times 2\) so
\[\sqrt[3]{16}=\sqrt[3]{8}\times \sqrt[3]{2}=2\sqrt[3]{2}\]

Answer 7

so first term in simplest radical form is
\[3m\sqrt[3]{2m}\] and second term in simplest radical form is
\[2m\sqrt[3]{2m}\] and since these are like terms you can combine them as follows:

\[3m\sqrt[3]{2m}+2m\sqrt[3]{2m}=5m\sqrt[3]{2m}\]

Answer 8

you got this?

Answer 9

ok I think I finally got it, I was making sure before I typed anything, you helped me break it down so that I understood how to do it. OMG TY sooooo much

Answer 10

yw
glad to help