Hi, there--

You leave answers as a radical when the problem says "give an exact answer," or "do not 
simplify."

You write the answer as a number (usually a decimal) when the problem asks you for an 
approximation, or when you are working on a real-word problem and you need a 
measurement.

WHY?
By definition, radicals are irrational unless the number under the radical is a perfect square. 
This means that they cannot be written as an equivalent fraction or decimal.

For example,  cannot be written as an exact whole number, fraction, or decimal. 
There is no decimal number you can multiply by itself to get 27.

When you want an exact answer, you need to stop there; the  is exactly .

Sometimes, that's not very useful.  For example, If I say that the doorway is exactly 
 feet high, that doesn't tell you much. A measuring tape does not have square 
roots on it. In this case, we would want an approximation.

The  is about 5.2 feet. You can get a decimal approximation for square roots by using your calculator.

You can also say which two whole numbers the square root is between. Here's how that works:

The perfect square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, and so on.

The number  is between 5 and 6 because 27 is between the perfect squares 25 
and 36.

I hope this helps. Feel free to email me if you have questions about this. I can explain further.

Mrs.Figgy
math.in.the.vortex@gmail.com