SOLUTION: sqrt 0f 450 divided by the sqrt of 1800 simplify

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Question 398495: sqrt 0f 450 divided by the sqrt of 1800 simplify
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

With expression like this, a square root over a square root, I like to use the following procedure:
  1. Use the property to combine the two square roots into a single square root.
  2. Reduce the fraction inside the square root, if possible.
  3. If the denominator is not a perfect square, then multiply the numerator and denominator by some number so that the denominator becomes a perfect square.
  4. Use the same property as step 1, only in reverse, to split the square root into a square root over a square root.
  5. Simplify the square roots.

Let's see this in action.
1) Combine the square roots:

2) Reduce the fraction inside. Since 450*4 = 1800 this fraction reduces to:

3) If the denominator is is not a perfect square, then make it one. Since 4 is a perfect square, we can skip this step.
4) Split the square root:

Since both 1 and 4 are perfect squares, both the numerator and denominator simplify to nice whole numbers:


Note 1: The procedure I've described is not the only way to simplify your expression. But it is pretty efficient at handing square roots over square roots.
Note 2: Any procedure used correctly should simplify your expression to a 1/2.
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