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

1 Answer
Lotusbluete
Feb 4, 2016

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!

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