Question

I need help dividing radicals! How would you do 3√135m^5 / √21m^3? Could someone walk through it step by step?

Answer 1

is it
\[\frac{\sqrt[3]{135m^5}}{\sqrt{21m^3}}\] or maybe\[\frac{\sqrt[3]{135m^5}}{\sqrt[3]{21m^3}}\]

Answer 2

or even
\[\frac{3\sqrt{135m^5}}{\sqrt{21m^3}}\]

Answer 3

The last one!

Answer 4

Sorry its not very clear

Answer 5

this one \[\frac{3\sqrt{135m^5}}{\sqrt{21m^3}}\] ?

Answer 6

Yes, that one :)

Answer 7

ok so not the "cubed root"
first step is to cancel common factors top and bottom, since this is the same as
\[3\sqrt{\frac{135m^5}{21m^3}}\]

Answer 8

since \(\frac{135}{21}\) reduces to \(\frac{45}{7}\) and \(\frac{m^5}{m^3}=m^2\) you get
\[\frac{3\sqrt{45m^2}}{7}\]

Answer 9

no typo there

Answer 10

you get
\[3\sqrt{\frac{45m^2}{7}}\]

Answer 11

then since \(\sqrt{m^2}=m\) this is the same as
\[\frac{3m\sqrt{45}}{\sqrt{7}}\]

Answer 12

I'm following so far.

Answer 13

also since \(45=9\times 5\) you have \(\sqrt{45}=\sqrt{9}\sqrt{5}=3\sqrt{5}\) bringing you to
\[\frac{9m\sqrt{5}}{\sqrt{7}}\]

Answer 14

and finally if you want to get rid of the radical in the denominator (to write in "simplest radical form") multiply top and bottom by \(\sqrt{7}\) to get \[\frac{9m\sqrt{5}}{\sqrt{7}}\times \frac{\sqrt{7}}{\sqrt{7}}\]
\[=\frac{9m\sqrt{35}}{7}\]

Answer 15

Thats the answer, I just missed a few steps. Thanks so much for your help!