Question

"Question 1 1Classify the following numbers as rational or irrational:
(i) 2-5^(1/2)
(ii) (3 + 23^(1/2)) - 23^(1/2)
(iii) [2.7^(1/2)] / [7.7^(1/2)]
(iv) 1/2^(1/2)
(v) 2π

Class 9 - Math - Number Systems Page 24"

Answer 1

Some facts about real numbers which are also true:

• The sum or difference of a rational number and irrational number is an irrational number.
• The multiplication or division of a non zero rational number with an irrational number is an irrational number

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Solution:

i) 2 -√5

Here 2 is a rational number and √5 is irrational number
We know that subtraction of a rational number and irrational number is always an irrational number.

Hence 2 - √5 is an irrational number.

ii) (3+√23) - √23

3 + √23-√23= 3

Hence , 3 is a rational number.

iii) 2√7 / 7√7

2√7 / 7√7 = 2/7

Hence , 2/7 is a rational number.

iv) 1/√2

Here, 1 is a rational number &√2 is an irrational number . We know that division of a rational number and irrational number is always an irrational number.

Hence, 1/√2 is an irrational number.

v) 2π

Here, 2 is a rational number & π is an irrational number. We know that product of a nonzero rational number and an irrational number is always an irrational number.

Hence, 2π rational number.


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Hope this will help you...

Answer 2

I think this is enough
here 5^(1/2) , 27^(1/2) , 77^(1/2) , 2^ (1/2) , π are irrational