Show how √6 can be represented on the number line.

Representing √6 on the Number Line

To locate √6 on the number line, we start by expressing 6 as a sum of two perfect squares:

• •  √6 = √(5)² + (1)²

From Pythagoras Theorem √5 can be represented as √5 = √2^2 +1 Step 1: Mark point A at 0 and point B at 2 on the number line, such that AB = 2 units. Step 2: Draw a line segment BC = 1 unit perpendicular to AB at point B. Step 3: Join points A and C. We obtain AC = √5. Step 4: Draw a line segment CD = 1 unit perpendicular to AC at point C. Step 5: Join points A and D. We get AD = √6. Step 6: Draw a circle with A as the center and AD as the radius. It intersects the number line at point E. Step 7: Point E represents √6 on the number line.