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Simplify sqrt(x*sqrt(x*sqrt(x))). Express your answer in simplest radical form in terms of x

 Aug 5, 2022
 #1
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x sqrt (x)  =  x^(1 +1/2)  =  x^(3/2)

 

sqrt (x * sqrt (x))  =  sqrt (x^3/2) =  (x^3/2)^(1/2)   =  (x^3/4)

 

x * [sqrt (x *sqrt (x) ]   =  x*  x^(3/4) =  x ^(1 + 3/4)  = x^(7/4)

 

sqrt [ x *  [sqrt (x *sqrt (x)] ] =   (x^7/4)^(1/2 ) =    x^(7/8)

 

 

cool cool cool

 Aug 6, 2022

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