SOLUTION: square root of 48 x to the power of 3 y to the power of 5 over the square root of 18 x to the power of 5

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Question 629523: square root of 48 x to the power of 3 y to the power of 5 over the square root of 18 x to the power of 5
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

While there are manyu ways to to do, the way I like to simplify expressions like this, a square root over a square root, is:
  1. Use the property of radicals change the fraction of square roots into the square root of a fraction.
  2. Reduce the fraction. (If you're clever and you know what the next step is, then you may choose not to reduce the fraction fully. I'll show you what I mean later.)
  3. If there is still a denominator, then...
    1. Make it a perfect square.
    2. Use the property again, this time in reverse, to create a fraction of square roots.
  4. Simplify any remaining square roots.
Let's see this in action:

1. Merge the square roots


2. Reduce


3.1 Make the denominator a perfect square:



3.2 Split the square root


4. Simplify





P.S. Now I'm going to repeat the first two steps using "clever" reducing:
1. Merge the square roots


2. Reduce
I'm still going to reduce the x's as before. But instead of dividing the numerator and denominator by 6 like I did above, I am going to just divide by 2:

The fraction is not fully reduced, But look at the denominator! It is now a perfect square. So by thinking ahead we can skip step 3.1.
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