How do you simplify #sqrt(2x)(sqrt(8x)-sqrt32)#?

1 Answer
Oct 4, 2017

Answer:

See a solution process below:

Explanation:

First, rewrite we can expand the expression by multiplying each term in parenthesis by the term outside the parenthesis:

#sqrt(color(red)(2x))(sqrt(color(blue)(8x)) - sqrt(color(blue)(32))) =>#

#(sqrt(color(red)(2x)) * sqrt(color(blue)(8x))) - (sqrt(color(red)(2x)) * sqrt(color(blue)(32)))#

We can next use this rule for radicals to execute the two multiplication operations:

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

#(sqrt(color(red)(2x)) * sqrt(color(blue)(8x))) - (sqrt(color(red)(2x)) * sqrt(color(blue)(32))) =>#

#sqrt(color(red)(2x) * color(blue)(8x)) - sqrt(color(red)(2x) * color(blue)(32)) =>#

#sqrt(16x^2) - sqrt(64x) =>#

#4x - sqrt(color(red)(64) * color(blue)(x)) =>#

#4x - (sqrt(color(red)(64)) * sqrt(color(blue)(x))) =>#

#4x - 8sqrt(x)#