LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

REAL NUMBERS

__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**