Page 12 - Mathematics Class - X

9. OQPS is a square and OP is its diagonal. Length of OR is equal to the length of the diagonal of
square OQPS. Therefore, the length of a diagonal of given square can be represented on a number line.

INFERENCE

We can represent an irrational numbers on a number line applying the pythagoras theorem and a graph paper.

OBSERVATIONS
Actual measurement,
OP = __________, OR = __________

EXTENDED TASK
Length and breadth of a rectangle are 6 cm. and 3 cm. respectively. Represent the length of its diagonal on the
number line.

APPLICATION
Irrational numbers are important in architecture and design to create beautiful proportions is furniture.

Viva-Voce

1. What do you understand by rational number?
p
Ans. A rational number is a type of real number, which is in the form of q where p and q both are the integers
and q ≠ o.
2. What is the definition of irrational number?
Ans. An irrational number is a number which can not be expressed in form of p/q where p and q both are the
integers and q ≠ o. For example, 2, 3, 5 are an irrational numbers.
3. Is π a rational number?
Ans. No, π is not a rational number. It is an irrational number and its value equals to 3.1415 ...... .

4. Do you think that 9 is an irrational number?
Ans. No, 9 is a rational number

Because, 9 = 3 2 = 3
1 1 p
3
Here, is of the form q
1
So, 9 is a rational number
5. If we multiply a rational number with an irrational number then what will be the product?

Ans. Rational number × Irrational number = Irrational number
Product will be an irrational number.
6. Is 0 is a rational number?
Ans. Yes, 0 is a rational number because it is an integer that can be written in any form such as 0/1, 0/2 where
denominator is a non-zero integer.
p 0
So, q = . Hence 0 is a rational number.
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