SOLUTION: -sqrt(18)/sqrt(12) The answer is -sqrt(6)/2 I am having beyond complications solving this problem. I have the answer, but I need help on how to actually solve it. Thanks!

Algebra ->  Radicals -> SOLUTION: -sqrt(18)/sqrt(12) The answer is -sqrt(6)/2 I am having beyond complications solving this problem. I have the answer, but I need help on how to actually solve it. Thanks!       Log On


   

Question 851430: -sqrt(18)/sqrt(12)
The answer is -sqrt(6)/2
I am having beyond complications solving this problem. I have the answer, but I need help on how to actually solve it. Thanks!

Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
Hello. Here is how you would solve your problem.

-sqrt%2818%29%2Fsqrt%2812%29

First, simplify the radicals in the numerator and denominator:

-sqrt%2818%29 can be reduced to -3%2Asqrt%282%29

sqrt%2812%29 can be reduced to 2%2Asqrt%283%29

Now, you are left with:

%28-3%2Asqrt%282%29%29%2F%282%2Asqrt%283%29%29

You now have to rationalize the denominator, since you cannot have an irrational number, such as a root, in the denominator of a fraction. To do this, we can multiply both the numerator and denominator by sqrt%283%29. This will eliminate the root from the denominator:

%28-3%2Asqrt%282%29%2Asqrt%283%29%29%2F%282%2Asqrt%283%29%2Asqrt%283%29%29

This gives us:

%28-3%2Asqrt%286%29%29%2F%282%2A3%29 ----->

%28-3%2Asqrt%286%29%29%2F6

Finally, we can reduce the fraction down, since both the numerator and denominator of the fraction are divisible by 3. This gives us the final answer of:

-sqrt%286%29%2F2