proove that 2-3*root5 is an irrational number ! please dont just give the solution , explain too how to do the solution of these types of questions

It is very easy to solve these types of questions. You just need to understand what is an irrational number and what is a rational number. 

 

Irrational number is a number that CAN'T be represented by a ratio of 2 integer while rational number (the opposite) is a number that can be represented by a ratio of 2 integer.
example: 0.25 is a rational number since it can be represented by 25/100 or 1/4 while phi (3.14159...) can't be represented as a ratio of 2 integer therefore phi is an irrational number.

Also usually, an equation involving an irrational number will result in an irrational number, unless the irrational number are divided by themselves or by all their irrational factor (which make their value be 1).

Now, since  is an irrational number .  is also an irrational number.

negative of an irrational number is also an irrational.

thus  is also an irrational number.

since 2 is a rational number and sum of rational number and irrational number is an irrational number.

thus  is an irrational number.