Question

6.
Which of the following is a rational number?
a) 0.123456....
b) V23
C) V36
d) 2V3​

Answer 1

Answer: (c)√36

Step-by-step explanation: because the value of √36 is 6.

The value of other numbers are irrational which means the values are non terminating and non reccuring

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Answer 2

√36 is Rational number in given numbers 0.123456.... , √23 , √36 and 2√3​

Given : Real numbers

a) 0.123456....

b) √23

C) √36

d) 2√3​

To Find :

Which is Rational number

Solution:

Rational numbers are real numbers which can be written in the form p/q where p and q are integers and q≠0

All real numbers which are not rational  are irrationals.

Rational numbers are terminating decimals or non terminating recurring decimal.

Irrational numbers are non terminating non-recurring decimals

a) 0.123456....

non terminating non-recurring decimals

Hence irrational number

b) √23

square root of non perfect square number

Hence irrational number

C) √36

= 6

= 6/1  

p/q form where p and q are integers and q≠0

Hence Rational Number

d) 2√3​

√3​ is square root of non perfect square number

Hence  √3​ is irrational

2 is rational

"Product of non zero rational number and irrational number is always irrational"

=> 2√3​ is irrational number  

Option C) √36 is Rational number

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