Simplify:
#(7sqrt3+2sqrt6)^2#
Use the formula for the square of a sum:
#(a+b)=a^2+2ab+b^2#,
where:
#a=7sqrt3#, #b=2sqrt6#
#(7sqrt3+2sqrt6)^2=#
#(7sqrt3)^2+(2xx7sqrt3xx2sqrt6)+(2sqrt6)^2#
Apply multiplication distributive property: #(ab)^2=a^2b^2#
Simplify #(7sqrt3)^2# to #7^2(sqrt3)^2#.
#7^2(sqrt3)^2+(2xx7sqrt3xx2sqrt6)+(2sqrt6)^2#
Simplify #7^2# to #49#.
#49(sqrt3)^2+(2xx7sqrt3xx2sqrt6)+(2sqrt6)^2#
Apply rule: #(sqrta)^2=a#
Simplify #(sqrt3)^2# to #3#.
#49xx3+(2xx7sqrt3xx2sqrt6)+(2sqrt6)^2#
Simplify #49xx3# to #147#.
#147+(2xx7sqrt3xx2sqrt6)+(2sqrt6)^2#
Apply multiplication distributive property: #(ab)^2=a^2b^2#
#147+(2xx7sqrt3xx2sqrt6)+2^2(sqrt6)^2#
Simplify #2^2# to #4#.
#147+(2xx7sqrt3xx2sqrt6)+4(sqrt6)^2#
Apply rule: #(sqrta)^2=a#
Simplify #(sqrt6)^6# to #6#.
#147+(2xx7sqrt3xx2sqrt6)+4xx6#
Simplify #4xx6# to #24#.
#147+(2xx7sqrt3xx2sqrt6)+24#
Apply rule: #sqrtasqrtb=sqrt(axxb)#
Simplify #2xx7sqrt3xx2sqrt6# to #2xx7xx2sqrt(3xx6)#.
#147+(2xx7xx2sqrt(3xx6))+24#
Simplify #sqrt(3xx6)# to #sqrt18#.
#147+(2xx7xx2sqrt18)+24#
Prime factorize #sqrt18#.
#147+(2xx7xx2sqrt(2xx3^2))+24#
Apply rule: #sqrt(a^2)=a#
#147+(2xx7xx2xx3sqrt2)+24#
Simplify #2xx7xx2xx3sqrt2# to #84sqrt2#.
#147+84sqrt2+24#
Simplify #147 +24# to #171#
#171+84sqrt2#
