SOLUTION: I don't know how to write out the problem, but I'll try my best so you can understand it. The problem I have is -3 square root of 20 times square root of 15. The answer I came to

Algebra ->  Radicals -> SOLUTION: I don't know how to write out the problem, but I'll try my best so you can understand it. The problem I have is -3 square root of 20 times square root of 15. The answer I came to       Log On


   

Question 73433: I don't know how to write out the problem, but I'll try my best so you can understand it. The problem I have is -3 square root of 20 times square root of 15. The answer I came to was -30 square root of 3. Is this correct?
Found 2 solutions by Cintchr, bucky:
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+-3sqrt%2820%29+%2A+sqrt%2815%29+
Since you are multiplying, you can combine your square roots right away
+-3sqrt%2820%2A15%29+
Break the 20 and the 15 up into Prime factors
+-3sqrt%282%2A2%2A5%2A5%2A3%29+
Since we are doing square roots, we pull numbers out from under the radical in pairs, but only one stays.
+-3%282%29%285%29sqrt%283%29+
Multiply the co-efficients
+-30sqrt%283%29+
You were right!!

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how I understood what you said ... your problem is:
.
%28-3%29%2Asqrt%2820%29%2Asqrt%2815%29
.
and you need to simplify it.
.
Congratulations, your answer is correct! You can check your work and see if you did it
like I did.
.
Here's how I did it:
.
Notice that 20 can be factored into 4 times 5 and 15 can be factored into 3 times 5.
.
Substitute these values into the problem statement to get:
.
%28-3%29%2Asqrt%284%2A5%29%2A+sqrt%283%2A5%29
.
Now, using the rule that sqrt%28a%2Ab%29+=+sqrt%28a%29%2A+sqrt%28b%29:
.

.
Notice that sqrt%284%29+=+2 and that sqrt%285%29%2Asqrt%285%29+=+5. We can make these
substitutions to get:
.
%28-3%29%2A2%2A5%2Asqrt%283%29
.
Multiplying out the leading constants ((-3)*2*5) = -30 and the answer becomes:
.
%28-30%29%2Asqrt%283%29
.
Good job! Keep up the good work!