Question

Represent √3 , √5 on the number line (Square Root spiral)

Answer 1

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Step 1: Draw a line OA on the negative side of the number line of unit length.
Step 2: Draw a ray AB such that ∠BAO = 60°

Step 3: Draw a line OC perpendicular to the number line which meets AB at C.

Step 4: Taking OC as radius and O as centre, draw an arc which cuts the positive number line at P.

Thus, P represents √3 on the number line.

Proof: In triangle OAC, tan 60° = OC/OA

, that is, OC = OA tan 60° = √3

Now, OP = OC = √3, (both are radii of same arc)