REAL Numbers
The set of Real numbers is the collection of rational & irrational numbers.
Properties or features of Real Numbers –
a) The sum, difference, and product of two real numbers are real numbers.
b) The division of a real number by a nonzero real number gives a real number.
c) Every real number has a negative real numbers. Zero ‘0’ is its own negative integers.
d) The sum, difference, product & quotient of a rational number and an irrational number are irrational.
5 is a rational number and √3 is an irrational number then 5 + √3, 5 - √3, 5√3, 5/√3, √3/5 are all irrational numbers.
e) The sum, difference, product, and quotient of two irrational numbers need not be irrational number.
There are some example are given below for your understanding
1) (3 + √2) + ( 3 - √2) = 6, is not irrational number.
2) (√5 + 2 ) – ((√5 – 2 ) = 4, is not irrational number.
3) (3 + √2) X ( 3 - √2 ) = 9² - (√2)² = 9 – 4 = 5, which is not irrational number
f) Given two real numbers x & y, √x . √y = √xy
x
√x / √y = √-------
y
and (√x)² = √x.√x = √x . x = x