Number Systems - Geometrical Method

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Steps to represent √x on the number line:

1. Draw a line and mark point A.
2. Mark a point B on the line such that AB=x units
3. From B at unit distance mark point C.
4. Find mid-point of AC and mark it as O.
5. Draw a semi- circle with radius O and radius OC.
6. Draw a line perpendicular to AC at point B, passing through and intersecting semi-circle at D. Length BD  is equal to  √x.
7. Now BD as radius and B as centre draw an arc it cuts number line at a point say E, distance from B to E represents √x.

Examples:
Represent √9.3 on the number line [NCERT]
Represent √10.25 on the number line