How do you simplify #3w ^ { 2} \sqrt { 72w } - \sqrt { 50w ^ { 5} }#?

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Answer 1 · 2017-11-15T06:15:26

#=> 13 w^2 sqrt(2w)#

#3w ^ { 2} \sqrt { 72w } - \sqrt { 50w ^ { 5} }#

#=> 3w ^ { 2} \sqrt { 9xx4xx2xxw } - \sqrt { 25xx2xxw ^ { 5} }#

#=> 3w ^ { 2} xx3xx2\sqrt { 2w } - 5\sqrt { 2wxxw ^ { 4} }#

#=> 18w ^ { 2}\sqrt { 2w } - 5w^2\sqrt { 2w}#

#=> (18- 5)w ^ { 2}\sqrt { 2w } #

#=> 13 w^2 sqrt(2w)#

Answer 2 · 2017-11-15T06:20:46

#13w^2sqrt(2w)#

Pull the perfect squares out of the square roots

#3w^2sqrt(72w)-sqrt(50w^5)#

#=3w^2sqrt(36*2w)-sqrt(25*2w^5)#

#=3w^2sqrt(36)sqrt(2w)-sqrt(25)sqrt(2w^5)#

#=3w^2*6sqrt(2w)-5sqrt(2w^5)#

Next, you can simplify the #w^5# by rewriting it as #w^(4+1)=w^4w^1#.

#=18w^2sqrt(2w)-5sqrt(2w^4w^1)#

#=18w^2sqrt(2w)-5w^2sqrt(2w)#

The #sqrt(2w)# factors out of both terms

#=(18w^2-5w^2)sqrt(2w)#

The terms on the left simplify

#=13w^2sqrt(2w)#