How do you evaluate #6\sqrt { 10} + 6\sqrt { 80} - 4\sqrt { 72} - 7\sqrt { 180}#?

1 Answer
turksvids
Jan 11, 2018

#=6sqrt(10)-24sqrt(2)-18sqrt(5) #

Explanation:

#sqrt(10)# does not reduce.
#sqrt(80)=sqrt(16*5)=sqrt(4^2*5)=4sqrt(5)#
#sqrt(72)=sqrt(36*2)=sqrt(6^2*2)=6sqrt(2)#
#sqrt(180)=sqrt(36*5)=sqrt(6^2*5)=6sqrt(5)#, so:

#6sqrt(10)+6sqrt(80)-4sqrt(72)-7sqrt(180) #

#=6sqrt(10)+6(4sqrt(5))-4(6sqrt(2))-7(6sqrt(5)) #

#=6sqrt(10)+24sqrt(5)-24sqrt(2)-42sqrt(5) #

#=6sqrt(10)-24sqrt(2)-18sqrt(5) #

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