SOLUTION: I need to perform the indicated operations: 3 sqrt [3] + 2 sqrt [27] - sqrt [12] Thanks for anyone that can help.

Algebra ->  Radicals -> SOLUTION: I need to perform the indicated operations: 3 sqrt [3] + 2 sqrt [27] - sqrt [12] Thanks for anyone that can help.      Log On


   

Question 152340This question is from textbook Intermediate Algebra
: I need to perform the indicated operations:
3 sqrt [3] + 2 sqrt [27] - sqrt [12]
Thanks for anyone that can help. This question is from textbook Intermediate Algebra

Found 2 solutions by jim_thompson5910, nabla:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3%2Asqrt%283%29%2B2%2Asqrt%2827%29-sqrt%2812%29 Start with the given expression



3%2Asqrt%283%29%2B2%2A3%2Asqrt%283%29-sqrt%2812%29 Simplify sqrt%2827%29 to get 3%2Asqrt%283%29. Note: If you need help with simplifying square roots, check out this solver.


3%2Asqrt%283%29%2B2%2A3%2Asqrt%283%29-2%2Asqrt%283%29 Simplify sqrt%2812%29 to get 2%2Asqrt%283%29.


3%2Asqrt%283%29%2B6%2Asqrt%283%29-2%2Asqrt%283%29 Multiply 2 and 3 to get 6.

Since we have the common term sqrt%283%29, we can combine like terms


%283%2B6-2%29sqrt%283%29 Combine like terms. Remember, 5x%2B3x-4x=%285%2B3-4%29x=4x


7%2Asqrt%283%29 Now simplify 3%2B6-2 to get 7


So 3%2Asqrt%283%29%2B2%2Asqrt%2827%29-sqrt%2812%29 simplifies to 7%2Asqrt%283%29.


In other words, 3%2Asqrt%283%29%2B2%2Asqrt%2827%29-sqrt%2812%29=7%2Asqrt%283%29

Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
All we want to do here is take out perfect squares and combine. See as follows:
3sqrt(3)+2sqrt(9*3)-sqrt(4*3)=3sqrt(3)+6sqrt(3)-2sqrt(3)=7sqrt(3)