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Classroom activity(Constructing the 'square root spiral'): Take a large sheet of paper and construct the 'square root spiral' in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length. Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn1Pn by drawing a line segment of unit length perpendicular to OPn1. In this manner, you will have created the points P2,P3,.......,Pn,....., and joined them to create a beautiful spiral depicting 2,3,4,.......
463539_f33373d9618a4192a1e6c2108fdf088c.png

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Solution

Starting with point O, draw a line segment OP1 of unit length.
Now draw a line segment P1P2 perpendicular to OP1 again of unit length.
Here always we need to keep in mind that the measure of the line segment would always be a constant, i.e., 1 unit.
Now again daw a line segment P2P3 perpendicular to OP2 of unit length.
Again draw a line segment P3P4 perpendicular to OP3.
In this way, we have formed a figure as shown in figure.

492355_463539_ans_606c81a07c184d30b867b6eb513acea0.png

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