Question #7bc10

1 Answer
Mar 30, 2017

Answer:

#sqrt3#

Explanation:

#9sqrt8 = 9sqrt(2^3) = 3^2*2^(3/2)#
#6sqrt6 = 3*2*sqrt(3*2) = 3^1*2^1*3^(1/2)*2^(1/2) = 3^(3/2)*2^(3/2)#

#therefore# #(9sqrt8) / (6sqrt6) = (3^2*2^(3/2))/(3^(3/2)*2^(3/2))#

#= (3^(2 - 3/2)) * (2^(3/2 - 3/2))#
#= 3^(1/2)*1 = 3^(1/2) =# # sqrt(3) #