How do you solve #3(sqrt12)+4(sqrt18)#?

1 Answer
May 13, 2017

Answer:

See a solution process below:

Explanation:

First, use this rule of radicals to rewrite the expression:

#sqrt(a * b) = sqrt(a) * sqrt(b)#

#3(sqrt(12)) + 4(sqrt(18)) =>#

#3(sqrt(4 * 3)) + 4(sqrt(9 * 3)) =>#

#3(sqrt(4) * sqrt(3)) + 4(sqrt(9) * sqrt(3)) =>#

#3(2 * sqrt(3)) + 4(3 * sqrt(3)) =>#

#6sqrt(3) + 12sqrt(3)#

We can now factor a #sqrt(3)# out of each term and calculate the result:

#6sqrt(3) + 12sqrt(3) =>#

#(6 + 12)sqrt(3) =>#

#18sqrt(3)#

Or

#31.177# rounded to the nearest thousandth.