How do you simplify #sqrt(7x)(sqrt x-7sqrt 7)#?

1 Answer
Feb 4, 2016

Answer:

#sqrt(7) x - 49sqrt(x)#

Explanation:

First of all, expand by multiplying #sqrt(7x) * sqrt (x)# and #sqrt(7x) * 7 sqrt(7)# respectively:

#sqrt(7x) (sqrt(x) - 7 sqrt(7)) = sqrt(7x) * sqrt (x) - sqrt(7x) * 7 sqrt(7)#

... you can express #sqrt(7x)# as #sqrt(7) * sqrt(x)#...

# = sqrt(7) * color(blue)(sqrt(x) * sqrt (x)) - color(orange)(sqrt(7)) * sqrt(x) * 7 * color(orange)(sqrt(7))#

# = sqrt(7) * color(blue)((sqrt(x))^2) - color(orange)((sqrt(7))^2) * sqrt(x) * 7 #

... the operations squaring and taking the square root "eliminate each other"...

# = sqrt(7) * x - 7 * sqrt(x) * 7#

# = sqrt(7) x - 49sqrt(x)#

Hope that this helped!