Lab Manual: An Irrational Number - Class 9 PDF Download

Objective

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To represent an irrational number on the number line. (To represent √2 on number line).

Prerequisite Knowledge
Concept of Pythagoras theorem:

• In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides containing right angle.
• In a right angled triangle, if the base and perpendicular are of 1 unit each, the hypotenuse will be √(1² + 1²) = √2.
  Now, by using this concept, we will represent √2 on the number line.

Materials Required
A sheet of white paper, pencil, compass, eraser and ruler etc.

Procedure

• Draw a straight line X’OX on the white sheet of paper.
• Divide that line into equal parts from point O by paper folding activity taking each part as 1 unit. Mark the points as 1,2,3,…. etc.
• Draw the perpendicular at the point marked as ‘1’ by paper folding.
• Unfold the paper, and draw the line at the crease so formed. Mark a point A on this crease at 1 unit from line X’OX.
  
• Join O and A, we get OA = √2 units (By Pythagoras theorem).
• With O as centre, OA as radius, draw an arc intersecting the line X’OX at M.

Observation
We observe that OA = OM = √2 units.

Result
An irrational number √2 is represented on the number line.

Learning Outcome
Students can represent any irrational number on number line by using above method.
e.g., (√3)² = (√2)² + (1)²
At M, by paper folding draw perpendicular BM on the number line of 1 unit. Join OB. With O as centre and OB as radius draw an arc intersecting the line at N.
Thus OB = ON = √3 on the number line.

Activity Time
Represent √5, √7 on the number line.