Irrational Numbers on the Number Line P3

Remember this problem?

Consider the roots of the first 9 Natural Numbers (√1 to √9), how many of them produce Irrational Numbers?

List them.  Graph their approximate location on a number line.

number-line-600x271

Explain how you determined where to place them on the graph.

 

Is √10 Rational or Irrational?  Explain how you know.  Where on the number line would you graph it?

 

Consider the roots √100 to √109, how many of them produce Irrational Numbers?

List them.  Graph their approximate location on a number line.

Blank Number Line

Is there any relationship of these root (√101 to √109) to the roots (√1 to √9) of the original problem?  Explain your thinking.

 

Is there another interval of 10 integers that when you take their square root, has a relationship similar to the original 9?

 

 

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