Page 11 - Mathematics Class - X

Unit 1
Unit 1
Unit 2 Number System
Number System
Number System
Number System
ACTIVITY 1.1

OBJECTIVE
To represent the square root of a natural number, 32 on a number line using graph paper.

MATERIALS REQUIRED

Pencil Nails Cardboard
Thread Drawing pins Graph paper

PRE-REQUISITE KNOWLEDGE

1. Knowledge of pythagoras theorem.
2. To express a given number as the sum of the squares of the two numbers.

THEORY

According to pythagoras theorem, in a right-angled triangle, square of the hypotenuse is equal to the sum of the
squares of other two sides.
i.e. (Hypotenuse) = (Base) + (Perpendicular) 2
2
2
PROCEDURE

1. Paste a chart paper on a cardboard of suitable size.
2. Paste a graph paper on the chart paper.

3. Draw the axes X'OX and Y'OY on the graph paper as shown in figure.

4 + () . So, mark a point P (4, 4) on the graph paper.
4. Let's take ( 32 ) 2 = () 2 4 2
5. Tie a thread from O to P by fixing the nails.
Y
6. Measure the length of thread.
7. Mark a point R on x-axis such that 6
OP = OR = Length of the thread. 5
8. Using pythagoras theorem, in right-angled 4 S P (4, 4)
∆OPQ,
3
(OP) = (PQ) + (OQ) 2
2
2
2
⇒ (OP) = 4 + 4 2
2
2
1
⇒ OR = 16 + 16 [Q OP = OR] Q
2
X' O R X
⇒ OR = 32 1 2 3 4 5 6 7
2
⇒ OR = 32 Y'
Thus, OP represents 32 and 32 is an irrational number.
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