How do you simplify #2sqrt54+5sqrt24#?

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Answer 1 · 2018-04-24T05:56:28

#16sqrt{6}#

#2sqrt{54} + 5sqrt{24}#

#54 = 2 times 3^3#
#24 = 2^3 times 3#

#2sqrt{2 times 3^3} + 5sqrt{2^3 times 3}#

#2 sqrt{ 3^2} sqrt{2 times 3}+ 5sqrt{2^2}sqrt{2 times 3}#

#(2 times 3) sqrt{2 times 3}+ (5 times 2)sqrt{2 times 3}#

#6sqrt{2 times 3} + 10sqrt{2 times 3}#

#6sqrt{6} + 10sqrt{6}#

#(6+10)sqrt{6}#

#16sqrt{6}#

Answer 2 · 2018-04-24T06:10:38

#= 16sqrt6#

Write the radicand as a product of its factors, if possible using a square number,

#2sqrt54 +5sqrt24#

#=2sqrt(color(blue)(9)xx6) +5sqrt(color(red)(4)xx6)#

#=2xxcolor(blue)(3)sqrt6 +5 xx color(red)(2)sqrt6" "larr# find the roots

#=6sqrt6 +10sqrt6" "larr# there are like terms

#= 16sqrt6#