  ### Home > GC > Chapter 9 > Lesson 9.2.2 > Problem9-68

9-68.

Unlike a straightedge, a ruler has measurement markings. With a ruler, it is fairly simple to construct a line segment of length $6$ cm or a line segment with length $3$ inches. But how can you construct a line segment of $\sqrt{2}\approx1.414213562\ldots$ centimeters? Consider this as you answer the questions below.

1. With a ruler, construct a line segment of $1$ cm.

2. What about $1.4$ cm? Adjust your line segment from part (a) so that its length is $1.4$ cm. Did your line get longer or shorter?

Draw the original line segment of $1$ cm, then add to it as directed.
Note that the line does not become that much longer if the change you're making is very small.

3. Now change the line segment so that its length is $1.41$ cm. How did it change?

4. Karen wants to draw a line segment is exactly $\sqrt{2}\approx1.414213562\ldots$ centimeters long. Is this possible? Why or why not?

The line will lengthen, but it will never be exactly $\sqrt{2}$