**Math Labs with Activity – Represent an Irrational Number on the Number Line**

**OBJECTIVE**

To represent an irrational number on the number line.

**Materials Required**

- A sheet of white paper
- A geometry box

**Theory**

**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.

We can write √2 = .

So, if the base and the perpendicular of a right-angled triangle measure 1 unit each, the hypotenuse will measure , or √2 units. We shall use this concept to represent the irrational numbers on the number line.

**Procedure**

**To represent √2 on the number line**

**Step 1:** Draw a straight line OX on the sheet of white paper. Starting from point O, mark points 1, 2, 3, … at equal distances of 1 unit (take 1 unit = 1 cm). Then, the line OX can be used as the number line.

**Step 2:** Fold the paper along the line that passes through the point marked T’ and cuts the line OX such that the part of line OX on one side of the fold falls over the other part. Make a crease and unfold the paper. From the point marked T’ draw a line of length 11 unit moving upwards along the crease. Mark the top end of this line as point M. Join OM. Then, clearly OM = √2 units (by Pythagoras’ theorem).

**Step 3:** With O as the centre and OM as the radius, draw an arc cutting the line OX at a point A as shown in Figure 3.1. Then, the point A represents the number √2 on the number line.

**Result**

Any irrational number can be represented on the number line (using the above method).

**Remarks:** The students may be asked to represent other irrational numbers such as 43,45, etc., on the number line.

**Note:**

- We have √3 =

So, in order to represent √3 on the number line, we have to take the horizontal line of length √2 units (already marked as point A in Figure 3.1) and the vertical line of length 1 unit and then draw the arc cutting the horizontal line. - We have √5 =

So, in order to represent √5 on the number line, we have to take the horizontal line of length 2 units and the vertical line of length 1 unit and then draw the arc cutting the horizontal line.

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