Rules: If two rational number are added , subtracted or divided, the result is always rational number.
Rules: The same is not true for irrational numbers. The sum , difference , quotients and products of irrational numbers are not always irrational.
e.g (√6) + (-√6) , (√2) – (√2) , (√3).( √3) and √17/√17 are rational numbers.

Important points to remember:
1) The sum or difference of a rational number and an irrational number is irrational .
2) The product or quotient of a non-zero rational number with an irrational number is irrational.
3) If we add , subtract , multiply or divide two irrational numbers , the result may be rational of irrational .
Other Inportant Points
If $a$ and $b$ are postive numbers, then
(i) $√{ab}$ = $√a.√b$
(ii) $√{a/b}$ = ${√a}/√b$
(iii) $(√a+√b)(√a-√b) = a -b $
(iv) $(a+√b)(a-√b) = a^2 -b $
(v) $(√a+√b)(√c+√d) = √{ac} + √{ad} + √{bc} +√{bd}
(vi) $(√a+√b)^2 $ = $a +2V{ab} +b $
Rationalisation the denominator

Rationalise the denominator of $1/√2$ Rationalise the denominator of $1/{2+√3}$ Rationalise the denominator of $5/{√3-√5}$ Rationalise the denominator of $1/{7+3√2}$