Represent \( \sqrt{3.5}, \sqrt{9.4}, \sqrt{10.5} \) on the Number Line
Construction Method:
Step 1:
Draw a number line and mark O (0) and A such that OA = 3.5 units.
Step 2:
At point A, draw a perpendicular AB of length 1 unit.
Step 3:
Join OB.
\[ OB = \sqrt{(3.5)^2 + 1^2} = \sqrt{3.5} \]
Mark this length on the number line.
Correct Construction Idea:
To construct \( \sqrt{3.5} \):
- Take OA = 2.5 units
- Draw perpendicular AB = 1 unit
- Join OB → OB = √3.5
To construct \( \sqrt{9.4} \):
- Take OA = 8.4 units
- Draw perpendicular AB = 1 unit
- Join OB → OB = √9.4
To construct \( \sqrt{10.5} \):
- Take OA = 9.5 units
- Draw perpendicular AB = 1 unit
- Join OB → OB = √10.5
Final Result:
The lengths \( \sqrt{3.5}, \sqrt{9.4}, \sqrt{10.5} \) can be marked on the number line using the above construction method.
Alternative (Approximate Values):
\[ \sqrt{3.5} \approx 1.87,\quad \sqrt{9.4} \approx 3.07,\quad \sqrt{10.5} \approx 3.24 \]
Mark these points appropriately on the number line.