SOLUTION: 3square root 12 + 4square root 3 = 8square root 5 - 2 square root 45 = Could you please explain how these are fully done. I am having a hard time understanding

Algebra ->  Radicals -> SOLUTION: 3square root 12 + 4square root 3 = 8square root 5 - 2 square root 45 = Could you please explain how these are fully done. I am having a hard time understanding       Log On


   

Question 128326: 3square root 12 + 4square root 3 =

8square root 5 - 2 square root 45 =
Could you please explain how these are fully done. I am having a hard time understanding how to do them. I thank you in advance and look forward to hearing from you.The question is not in any text and is only on a printed sheet.
Matthew
Found 2 solutions by checkley71, josmiceli:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
3SQRT12+4SQRT3=3SQRT(4*3)+4SQRT4SQRT3=3*2SQRT3+4SQRT3=(6+4)SQRT3=10SQRT3.
8SQRT5-2SQRT45=8SQRT5-8SQRT(9*5)=8SQRT5-(8*3)SQRT5=(8-24)SQRT5=-16SQRT5.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Asqrt%2812%29+%2B+4%2Asqrt%283%29 =
3%2Asqrt%284%2A3%29+%2B+4%2Asqrt%283%29 =
3%2A%28sqrt%284%29%2Asqrt%283%29%29+%2B+4%2Asqrt%283%29 =
Notice that sqrt%284%29+=+2
3%2A2%2Asqrt%283%29+%2B+4%2Asqrt%283%29 =
6%2Asqrt%283%29+%2B+4%2Asqrt%283%29=
Notice that sqrt%283%29 is a common factor
sqrt%283%29%2A%286+%2B+4%29 =
10%2Asqrt%283%29 answer
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8%2Asqrt%285%29+-+2%2Asqrt%2845%29 =
8%2Asqrt%285%29+-+2%2Asqrt%289%2A5%29 =
8%2Asqrt%285%29+-+2%2A%28sqrt%289%29%2Asqrt%285%29%29 =
8%2Asqrt%285%29+-+2%2A3%2Asqrt%285%29 =
8%2Asqrt%285%29+-+6%2Asqrt%285%29 =
Notice sqrt%285%29 is a common factor
sqrt%285%29%2A%288+-+6%29 =
2%2Asqrt%285%29 answer