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Plato Classroom Question #18

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Simplify $$\sqrt{256a^2b^4}$$.

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

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

Jan 26, 2018
edited by SpaceModo  Jan 26, 2018
edited by SpaceModo  Jan 26, 2018

#1
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4 x 4 x 4 x 4 = 256

=4ba^(1/2)

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

Jan 26, 2018
#2
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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.

$$\sqrt{256a^2b^4}\\ =\sqrt{16|a|b^2}\\ =4\sqrt{|a|}|b|\\ =|\;4b\sqrt{|a|}\;|\\ or\\ =|\;4b|a|^{1/2}\;|\\$$

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Jan 27, 2018
#3
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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
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Now you took it away 