Question

Represent `sqrt(10)` and `sqrt(20)` on the number line.

Answer 1

To represent `sqrt(10)` and `sqrt(20)` on the number line, follow this geometric construction method using the Pythagorean theorem:

Steps to construct `sqrt(10)` on the number line:

1. Draw a number line and mark a point O = 0.
2. From O, mark 10 units to the right: mark this point as A (10).
3. Find the midpoint of segment OA, which is at 5. Mark it as M.
4. With M as center and radius = MO, draw a semicircle.
5. Erect a perpendicular from point O to meet the semicircle. Call the intersection P.
6. The length of `OP = sqrt(10)`  ...(By Pythagoras’ theorem).
7. Use a compass to transfer OP onto the number line starting from 0.

Steps to construct `sqrt(20)`:

1. On the same number line, mark segment OA = 20 units.
2. Find the midpoint M = 10.
3. Draw semicircle with diameter OA.
4. Draw perpendicular from O to semicircle (as before).
5. That length `OP = sqrt(20)`.
6. Transfer this length to number line from 0.