How do you simplify #2 sqrt 8 - 2 sqrt 2#?

2 Answers
Mar 3, 2018

#2 sqrt(8) - 2 sqrt(2)#

#= 2 sqrt(4*2) - 2 sqrt(2)#

#=4 sqrt(2) - 2sqrt(2)#

#=2 sqrt(2)#

Mar 3, 2018

Answer:

See a solution process below:

Explanation:

First rewrite the radical on the left using this rule for radicals:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#2sqrt(8) - 2sqrt(2) =>#

#2sqrt(color(red)(4) * color(blue)(2)) - 2sqrt(2) =>#

#2sqrt(color(red)(4))sqrt(color(blue)(2)) - 2sqrt(2) =>#

#(2 * 2)sqrt(color(blue)(2)) - 2sqrt(2) =>#

#4sqrt(2) - 2sqrt(2)#

Now, we can factor out the common term to complete the simplification:

#(4 - 2)sqrt(2) =>#

#2sqrt(2)#