We already learnt that the collection of rational numbers and irrational numbers together is known as Real Numbers. This collection is denoted by R.
The sum, difference and the product of two rational numbers is always a rational number. The quotient of a division of one rational number by a non-zero rational number is a rational number. Rational numbers satisfy the closure property under addition, subtraction, multiplication and division.
The sum, difference, multiplication and division of irrational numbers are not always irrational. Irrational numbers do not satisfy the closure property under addition, subtraction, multiplication and division.
Real numbers satisfy the commutative, associative and distributive laws. These can be stated as :

• Commutative Law of Addition:
• Commutative Law of Multiplication:
• Associative Law of Addition:
• Associative Law of Multiplication:
• Distributive Law:  or

We can represent real numbers on the number line. The square root of any positive real number exists and that also can be represented on number line
The sum or difference of a rational number and an irrational number is an irrational number.
The product or division of a rational number with an irrational number is an irrational number.
Some of the basic identities involving square roots are:

a, b, c and d are positive real numbers.
The process of converting the denominator into a rational number is called rationalising the denominator.