How do you simplify #4sqrt112+ 5sqrt56- 9sqrt126#?

1 Answer
Jun 30, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite each of the radicals as:

#4sqrt(16 * 7) + 5sqrt(4 * 14) - 9sqrt(9 * 14)#

Next, use this rule for radicals to simplify the radicals:

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

#4sqrt(16)sqrt(7) + 5sqrt(4)sqrt(14) - 9sqrt(9)sqrt(14) =>#

#(4 * 4)sqrt(7) + (5 * 2)sqrt(14) - (9 * 3)sqrt(14) =>#

#16sqrt(7) + 10sqrt(14) - 27sqrt(14)#

Next, we can factor our common terms:

#16sqrt(7) + (10 - 27)sqrt(14) =>#

#16sqrt(7) + (-17)sqrt(14) =>#

#16sqrt(7) - 17sqrt(14)#

If necessary we can go this additional step:

#16sqrt(7) - 17sqrt(2 * 7) =>#

#16sqrt(7) - 17sqrt(2)sqrt(7) =>#

#(16 - 17sqrt(2))sqrt(7)#