Show how √17 can be represented on the number line.

Representing √17 on the Number Line

To represent √17 on the number line, follow these steps:

1. Draw a horizontal line segment OA of 4 units.
2. At point A, draw a perpendicular line AB of 1 unit.
3. Join OB. You now have a right-angled triangle OAB with ∠OAB = 90°.
4. Using the Pythagorean theorem, calculate OB:
   • OA² + AB² = OB²
   • 4² + 1² = OB²
   • 16 + 1 = OB²
   • OB² = 17
   • OB = √17
5. Take OB as the radius and O as the center. Draw an arc that intersects the number line at point P on the positive side.

The point P represents √17 on the number line.