Find an irrational number between 4,6

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Hint: Irrational numbers are categorized as all numbers except rational numbers. Irrational numbers are imaginary numbers. But we can obtain different types of numbers by applying various operations in mathematics such as multiplication and division. Hence, we can proceed by this methodology.

Complete step-by-step answer:

Mathematics is related to all the phenomena occurring in the world. When mathematical structures are good models of real phenomena mathematical reasoning can be used to provide insight or predictions about nature. In mathematics, the number system is the branch that deals with various types of numbers possible to form and easy to operate with different operators such as addition, multiplication and so on.
An irrational number is any real number other than a rational number.
As given in our problem, we have to find an irrational number which lies between 4 and 6.
Now, from the number system analysis, an irrational number between two numbers is the square root of both the numbers. It can be mathematically expressed as,
$a,b=\sqrt{a\times b}$
So, the irrational number between 4,6 $=\sqrt{4\times 6}=2\sqrt{6}$.
Therefore, option (a) is correct.

Note: It is a concept-based question. So, if the student tries to guess the number just by seeing the options given, he might get confused between option (a) and option (c). There is a slight possibility that the student might tick the incorrect option that is option (c).

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