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Simplify \(\sqrt[4]{256a^2b^4}\).

 

\(\color{green}\boxed{{\color{navy}x}~{\color{lightblue}x}^{\color{navy}y}~{\color{black}\frac{\color{navy}x}{\color{navy}y}}~\color{black}\sqrt{\color{navy}x}~~{\color{navy}+~~-~\times}}\)

\(\color{red}\boxed{{\color{black}\sqrt[\color{navy}y]{\color{lightblue}x}}}\)

SpaceModo  Jan 26, 2018
edited by SpaceModo  Jan 26, 2018
edited by SpaceModo  Jan 26, 2018
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4+0 Answers

 #1
avatar+12227 
0

4 x 4 x 4 x 4 = 256

 

=4ba^(1/2)

 

I do not know what the rest of your question means.....

ElectricPavlov  Jan 26, 2018
 #2
avatar+92206 
+2

I beg to differ just a little EP

By convention the answer must be positive and we do not know if a or b is pos or neg.

 

\(\sqrt[4]{256a^2b^4}\\ =\sqrt[2]{16|a|b^2}\\ =4\sqrt{|a|}|b|\\ =|\;4b\sqrt{|a|}\;|\\ or\\ =|\;4b|a|^{1/2}\;|\\\)

Melody  Jan 27, 2018
 #3
avatar+12227 
+1

Agree !   Melody is correct.... !      I was thinking about  a^2   and b^4   both being POSITIVE results...but that does not tell us if a or b are positive themselves !

ElectricPavlov  Jan 28, 2018
 #4
avatar+92206 
0

Please don't vote your answer down EP, it was just a small oversight.

I am the one who gave you that point and I thought you deserved it.

Now you took it away sad

Melody  Jan 28, 2018

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