How do you simplify #sqrt(8x^3) +sqrt(50x^5)- sqrt(18x^3)- sqrt( 32x^5)#?

1 Answer
Jun 2, 2018

Answer:

See a solution process below:

Explanation:

First, we can rewrite each of the radicals as:

#sqrt(4x^2 * 2x) + sqrt(25x^4 * 2x) - sqrt(9x^2 * 2x) - sqrt(16x^4 * 2x)#

Now, use this rule for radicals to rewrite the radicals and factor out a common term and group then combine like terms:

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

#(sqrt(4x^2) * sqrt(2x)) + (sqrt(25x^4) * sqrt(2x)) - (sqrt(9x^2) * sqrt(2x)) - (sqrt(16x^4) * sqrt(2x)) =>#

#2xsqrt(2x) + 5x^2sqrt(2x) - 3xsqrt(2x) - 4x^2sqrt(2x) =>#

#(2x + 5x^2 - 3x - 4x^2)sqrt(2x) =>#

#(2x - 3x + 5x^2 - 4x^2)sqrt(2x) =>#

#((2 - 3)x + (5 - 4(x^2)sqrt(2x) =>#

#(-1x + 1x^2)sqrt(2x) =>#

#(-x + x^2)sqrt(2x) =>#

#(x^2 - x)sqrt(2x)#

We can now factor out another common term:

#((x * x) - (1 * x))sqrt(2x) =>#

#(x - 1)xsqrt(2x)#