Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
385 views
asked in Mathematics by (21.7k points)

Examine, whether the following numbers are rational or irrational: 

(i) 7

 (ii) 4

 (iii) 2+ 3 

 (iv) 3 + 

 (v) 3+ 5 

 (vi) ( 2- 2 )2

 (vii) (2- 2)( 2+ 2) 

(viii) ( 2 +3) 2

 (ix) 5- 2

(x) 23 

(xi) 225 

(xii) 0.3796 

(xiii) 7.478478…… 

(xiv) 1.101001000100001……

Sarthaks Test For Class 7-12

1 Answer

0 votes
answered by (21.7k points)
selected by
 
Best answer

7 is not a perfect square root, so it is an irrational number.

 We have,

4 can be expressed in the form of , p/ q, so it is a rational number. 

The decimal representation of 4 is 2.0.

 2 is a rational number, whereas 3 is an irrational number. 

Because, sum of a rational number and an irrational number is an irrational number, so 2 +3  is an irrational number.

 2 is an irrational number. Also 3 is an irrational number. 

The sum of two irrational numbers is irrational.

  3+ 2 is an irrational number.

 5 is an irrational number. Also 3 is an irrational number. 

The sum of two irrational numbers is irrational.

 3 +5 is an irrational number.

We have,

Now, 6 is a rational number, whereas 42 is an irrational number. 

The difference of a rational number and an irrational number is an irrational number. 

So, 6- 42  is an irrational number. 

(2 - 2 ) is an irrational number.

 We have,

Since 2 is a rational number. 

(2 -2 )(2 +2) is a rational number.

We have,

The sum of a rational number and an irrational number is an irrational number, so 5+26  is an irrational number. 

(2 +3)2 is an irrational number. 

The difference of a rational number and an irrational number is an irrational number.

 5- 2 is an irrational number.

 23 = 4.79583152331........ 

225= 15 = 15/1

 Rational number as it can be represented in p/q form.

0.3796

As decimal expansion of this number is terminating, so it is a rational number. 

7.478478............ =7.bar 478 

As decimal expansion of this number is non-terminating recurring so it is a rational number. 

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

One Thought Forever

“There is a close connection between getting up in the world and getting up in the morning.“
– Anon
~~~*****~~~

Categories

...