Question

Which of the following is a rational number
a)0.123456..
b)
$\sqrt{23}$
c)
$\sqrt{36}$
d)
$2 \sqrt{3}$

​

Answer 1

The required "option c) $\sqrt{36}$" is correct.

Step-by-step explanation:

Rational number: The number can be written as $\dfrac{p}{q}$ form and $q\neq 0$.

Check options:

a) 0.123456...., is not a rational number.

b) $\sqrt{23}$

= 4.7958

33333....., is not a rational number.

c) $\sqrt{36}$

= 6 $\dfrac{6}{1}$, is a rational number.

d) $2\sqrt{3}$

$=2\times 1.73205080756887729352....$

, is not a rational number.

Hence, the required "option c) $\sqrt{36}$" is correct.

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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