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Assume that \(x\) is a positive real number. Then simplify

\[\large \sqrt[3]{x\sqrt{x}}\]

 Jan 22, 2021
 #1
avatar+266 
+6

\(\sqrt[3]{x\sqrt{x}} =\sqrt[3]{x^{1+\frac{1}{2}}} =\sqrt[3]{x^{\frac{3}{2}}}\)

 

cheekycheekycheeky

.
 Jan 22, 2021
 #2
avatar+116126 
+2

Note  that we can simplify DewdropDancer's answer just a little  more

 

(x^(3/2)) ^(1/3)  =  x^[ (3/2) * (1/3) ]  =  x^(1/2)   =  √ x

 

 

cool cool cool

CPhill  Jan 22, 2021
 #3
avatar+266 
+6

Ah yes, I missed that part.

DewdropDancer  Jan 22, 2021
 #4
avatar+116126 
+2

No prob.....you did 99% of the work   !!!!

 

 

cool cool cool

CPhill  Jan 22, 2021

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