The sum, difference, product and division of two rational number is a rational number.
The sum, difference, product and division of one rational number and one irrational number is an irrational number
The sum, difference product and division of two irrational numbers may be rational or irrational
The symbol used in 2, 5, etc is called as the radical sign
Some identities of square roots:
i) √ab = √a × √b
iii) ( √a+√b)(√a-√b) = a – b
iv)(a + √b) (a -√b) = a2 – b
v)(√a + √b) (√c+√d) = √ac + √ad + √bc + √bd
vi)(√a+√b)2 = a + 2√ab + b
When the denominator of an expression has term with a square root (√x) then the process of converting this irrational number into a rational number is called rationalization
Rationalization is done by multiplying both numerator and denominator by a suitable number.