what is 6 --- ^3√4

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what is 6 --- ^3√4

Mathematics
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what is |dw:1441484588912:dw|
how do you rationalize it?
|dw:1441486622928:dw|

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to rationalize the denominator means to get rid of the radical. multiply by 1 expressed as a fraction
before you continue can i just ask is there some sort of rule for what you did when you crossed out those fractions. Meaning, could i be able to do that with any sort of radical that i want to rationalize?
|dw:1441486781234:dw|
rules for exponents the nth root is the same as a fractional exponent.
the answer is supposed to be |dw:1441486876177:dw|
Or in decimal form, 3.7797631...
|dw:1441486898347:dw|
give me a minute
sure
|dw:1441487116337:dw||dw:1441487355866:dw|
I think I messed up on something @zepdrix please correct
Hey Angela :) In order to rationalize this thing, you'd like the power on the 4 to be a 1. I like the first step that Tricia applied, writing the 4 with a rational exponent.\[\large\rm \frac{6}{\sqrt[3]{4}}=\frac{6}{4^{1/3}}\]So we don't want a 1/3 power, we want a 1 power down there. What do we have to add to 1/3 to get 1?
hey :)) we have to add 2/3
Good good good. We would like 2/3 exponent, we'll leave the base the same. So we actually want to multiply top and bottom by \(\large\rm 4^{2/3}\) Our rules of exponents will give us \(\large\rm 4^{1/3}\cdot4^{2/3}=4^{1/3+2/3}\) in the denominator!
@zepdrix thanks
\[\large\rm \frac{6}{4^{1/3}}\left(\frac{4^{2/3}}{4^{2/3}}\right)=\frac{6\cdot4^{2/3}}{4^{3/3}}\]Ok with that step Angela? :o
|dw:1441488139781:dw|
6 * 42/3 divided by 4
\[\large\rm \frac{\color{orangered}{6}\cdot 4^{2/3}}{\color{orangered}{4}}\]Mmmm k good. This can be simplified a little bit further since 6 and 4 share a common factor.
so on the bottom we get 2 and the 6 turns into a 3?
\[\large\rm \frac{3\cdot4^{2/3}}{2}\]Yayyyy good job \c:/
so we don't need to do any further simplifying? because the answer in my book shows |dw:1441488618998:dw| @zepdrix
OH interesting :O Ok sec I think about it
Ok maybe this is a better route to take then..\[\large\rm \frac{6}{4^{1/3}}=\frac{3\cdot2}{4^{1/3}}=\frac{3\cdot2}{(2^2)^{1/3}}=\frac{3\cdot2}{2^{2/3}}\]
I'm rewriting the 6 as 3*2. I'm rewriting 4 as 2 squared. and then applying exponent rule, when we have a power and a power like that, we multiply. So 2 times 1/3 gave me 2/3 for the power on the 2.
\[\large\rm =\frac{3\cdot2^1}{2^{2/3}}\]And now we can apply one of our exponent rules from here: \(\large\rm \frac{x^{a}}{x^b}=x^{a-b}\) Do you see how we can apply that to the 2's?
yes thank you very much
@AngelaB97 sorry if we confuse you but hopefully you understand more about the rules of exponents and how to rationalize it is very easy to make mistakes if not careful
@zepdrix @triciaal thank you both for your help!
yay team \c:/
welcome anytime

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