Classroom activity (Constructing the ‘square root spiral’) : Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion.

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Chapter 1

NCERT

Class 9

Mathematics

Solutions

4. Classroom activity (Constructing the ‘square root spiral’) : Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion.

Question:

Classroom activity (Constructing the ‘square root spiral’) : Take a large sheet of paper andconstruct 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 P₁ P₂ perpendicular to OP₁ of unit length (see Fig.). 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 P_{n – 1} Pn by drawing a line segment of unit length perpendicular to OP_{n – 1}. In this manner, you will have created the points P2, P3 ........, Pn, ...... , and joined them to create a beautiful spiral depicting 2, 3, 4,...... Constructing square root spiral

Answer:

Take a large sheet of paper. First take a point O on it and draw a line segment OP₁ of unit length. Draw a line segment P₁P₂ perpendicular to point P₁ of unit length, now join OP₂. Line segment OP₂ represents √2 . Similarly, draw a line segment P₂P₃ of unit length on point P₂, then join OP₃ which represents √3 . Similarly draw a perpendicular line segment P₃P₄ on P₃ of unit length and join OP₄ which represents √4 . By doing a similar activity we get a square roof spiral showing √2 , √3 , √4 , ...

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(All Q's of this Chapter solved)

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