How do you simplify #sqrt48-sqrt45-sqrt75+sqrt150#?

1 Answer
Aug 30, 2017

Answer:

See a solution process below:

Explanation:

First, we can rewrite the expression as:

#sqrt(16 * 3) - sqrt(9 * 5) - sqrt(25 * 3) + sqrt(25 * 6)#

Next, we can use this rule of radicals to simplify each radical term individually:

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

#sqrt(color(red)(16) * color(blue)(3)) - sqrt(color(red)(9) * color(blue)(5)) - sqrt(color(red)(25) * color(blue)(3)) + sqrt(color(red)(25) * color(blue)(6)) =#

#sqrt(color(red)(16)) * sqrt(color(blue)(3)) - sqrt(color(red)(9)) * sqrt(color(blue)(5)) - sqrt(color(red)(25)) * sqrt(color(blue)(3)) + sqrt(color(red)(25)) * sqrt(color(blue)(6)) =#

#4sqrt(3) - 3sqrt(5) - 5sqrt(3) + 5sqrt(6)#

Now, we can group and combine like terms this way:

#4sqrt(3) - 5sqrt(3) - 3sqrt(5) + 5sqrt(6) =#

#(4 - 5)sqrt(3) - 3sqrt(5) + 5sqrt(6) =#

#-1sqrt(3) - 3sqrt(5) + 5sqrt(6) =#

#-sqrt(3) - 3sqrt(5) + 5sqrt(6)#

Or, we can group and combine like terms this way:

#4sqrt(3) - 3sqrt(5) + 5(-sqrt(3) + sqrt(6)) =#

#-3sqrt(5) + 4sqrt(3) + 5(sqrt(6) - sqrt(3)) =#