Class 09 To represent some irrational numbers on the number line.

 

Activity 2

OBJECTIVE                  

To represent some irrational numbers on the number line.                                                  

MATERIAL REQUIRED

Two cuboidal wooden strips, thread, nails, hammer, two photo copies of a scale, a screw with nut, glue, cutter.

 METHOD OF CONSTRUCTION

Two cuboidal wooden strips, thread, nails, hammer, two photo copies of a scale, a screw with nut, glue, cutter.

 1.   Make a straight slit on the top of one of the wooden strips. Fix another wooden strip on the slit perpendicular to the former strip with a screw at the bottom so that it can move freely along the slit [see Fig.1].

 2.   Paste one photocopy of the scale on each of these two strips as shown in Fig. 1.

 3.   Fix nails at a distance of 1 unit each, starting from 0, on both the strips as shown in the figure.

 4.   Tie a thread at the nail at 0 on the horizontal strip.

DEMONSTRATION

 11.   Take 1 unit on the horizontal scale and fix the perpendicular wooden strip at 1 by the screw at the bottom.

2.   Tie the other end of the thread to unit ‘1’ on the perpendicular strip. 

the horizontal strip to represent			√2 on the horizontal strip [see Fig. 1].
Similarly, to represent		√3 , fix the perpendicular wooden strip at  √2 and
repeat the process as above. To represent				√a , a > 1, fix the perpendicular
scale at	√a – 1 and proceed as above to get					√a .
OBSERVATION
On actual measurement:
a – 1 = ...........			√a =  ...........
APPLICATION
The activity may help in representing some irrational numbers  such as √2, √3, √4, √5, √6,√7.

. on the number line.

3.   Remove the thread from unit ‘1’ on the perpendicular strip and place it on

NOTE

You may also find   √a such as  √13 by fixing the perpendicular      strip at 3 on the horizontal strip       and tying the other end of thread               at 2 on the vertical strip.