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)) =#
