Show how √2 can be represented on the number line.

Representing √2 on the Number Line

1. Draw a line segment AB perpendicular to the number line, with AB being 1 unit in length.
2. Join point O (the origin) to point B.
3. Apply the Pythagorean theorem:
   • OB² = OA² + AB²
   • OB² = 1² + 1²
   • OB² = 1 + 1
   • OB² = 2
   • OB = √2
4. Using a compass, take point O as the center and OB as the radius. Draw an arc that intersects the number line.
5. The point where the arc intersects the number line represents a distance of √2 units from 0.

Thus, √2 is represented on the number line.