Question

prove that root 5 -3 root 2 is irrational number​

Answer 1

Solution :)

Let,

$(5 - 3 \sqrt{2}) \: \: be \: irrational$

and, its simplest form be a/b.

=> 5 -3 √2 = a/b

=> 3√2 =5-a/b

=>3√2 =(5b - a)/b

=> √2= (5b-a)/2b

Hence, a,b,5 and 2 are integers

therefore, (5b-a)/2b is also rational.

But, in fact, √2 is irrational.

Since, rational can't be equal to irrational.

Our assumption is wrong.