SOLUTION: Hi, I'm not sure how to type this hear. I'm having exams this week and I'm stumped on a couple of questions. I'll do the best I can. 3 square root of 250 minus 3 square root o

Algebra ->  Radicals -> SOLUTION: Hi, I'm not sure how to type this hear. I'm having exams this week and I'm stumped on a couple of questions. I'll do the best I can. 3 square root of 250 minus 3 square root o      Log On


   



Question 141524: Hi, I'm not sure how to type this hear. I'm having exams this week and I'm stumped on a couple of questions. I'll do the best I can.
3 square root of 250 minus 3 square root of 54 = ?
Thanks for your help!!

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Asqrt%28250%29-+3%2Asqrt%2854%29

Break 250 down into primes factors:

250+=+25%2A10+=+%285%2A5%29%2A%285%2A2%29+=+5%2A5%2A5%2A2

Break 54 down into prime factors:

54+=+9%2A6+=+%283%2A3%29%2A%283%2A2%29+=+3%2A3%2A3%2A2

Substitute these prime factorizations 
under the radical:

3%2Asqrt%285%2A5%2A5%2A2%29-+3%2Asqrt%283%2A3%2A3%2A2%29

Use parentheses to group all pairs of like factors:  

(We group by twos since it is a square root; 
if it were a cube root we would group by threes)

3%2Asqrt%28%285%2A5%29%2A5%2A2%29-+3%2Asqrt%28%283%2A3%29%2A3%2A2%29

The %285%2A5%29 is equivalent to 5%5E2 so we
take out only a single 5 out in front of the
radical:

3%2A5%2Asqrt%285%2A2%29-+3%2Asqrt%28%283%2A3%29%2A3%2A2%29

 The %283%2A3%29 is equivalent to 3%5E2 so we
take out only a single 3 out in front of the
radical:

3%2A5%2Asqrt%285%2A2%29-+3%2A3%2Asqrt%283%2A2%29

15sqrt%2810%29-9sqrt%286%29

Edwin