Find the value of #(2sqrt6)^6#?

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Answer 1 · 2017-08-16T13:30:10

#(2sqrt6)^6=13824#

#(2sqrt6)^6#

= #2^6xx(sqrt6)^6#

= #(2xx2xx2xx2xx2xx2)xx(sqrt(6xx6xx6xx6xx6xx6))#

= #64xxsqrt(ul(6xx6)xxul(6xx6)xxul(6xx6))#

= #64xx6xx6xx6#

= #64xx216#

= #13824#

Answer 2 · 2017-08-16T14:55:05

#13,824#

Use the laws of indices.

#(2 sqrt6)^6 = 2^6 xx (sqrt6)^6" "larr ((ab)^m = a^m b^m)#

#=2^6 xx (6)^(6/2)" "larr sqrtx = x^(1/2)#

#=2^6 xx 6^3#

#=(2xx2xx2xx2xx2xx2)xx (6xx6xx6)#

It helps to know the powers less than 1000 by heart.

#= 64 xx 216#

#=13,824#

Answer 3 · 2018-06-21T17:33:02

#13824#

#(2 sqrt 6)^6#

#:.=(2 xx6^(1/2))^6#

#:.=2^6 xx6^(6/2)#

#:.=64 xx 6^3#

#:.=64 xx 216#

#:.=13824#