What is the square root of 32^(2/3)?

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Answer 1 · 2015-09-19T12:35:30

$2root3(4)$

$sqrt(32)^(2/3)$

$=[(32)^(2/3)]^(1/2)$

$=(32)^(2/3*1/2)$

$=(32)^(1/3)$

$=(2^5)^(1/3)$

$=root3(2^5)$

$=root3(2^3 * 2^2)$

$=2root3(4)$

Answer 2 · 2015-09-19T12:44:30

$2xx2^(2/3)$

$sqrt(32^(2/3))=sqrt((2^5)^(2/3)$

$sqrt((2^5)^(2/3))=sqrt(2^(10/3)$

$sqrt(2^(10/3))=(2^(10/3))^(1/2)$

$(2^(10/3))^(1/2)=2^(10/6)$

$2^(10/6)=2^(5/3)$

$2^(5/3)=2^(1+2/3)=2xx2^(2/3)$

I hope that helps :)