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

2 Answers
Sep 19, 2015

#2root3(4)#

Explanation:

#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)#

Sep 19, 2015

#2xx2^(2/3)#

Explanation:

#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 :)