Question

prove that 3root2 - 2root3 is irrational
Please give answer with explanation​

Answer 1

Step-by-step explanation:

Let 3-√2 be a rational number hence, 3-√2=a/b,where a and b are integers and b is not equal to 0...

3-√2=a/b

√2=a/b-3

=√2=a-3b/b

here a-3b/b are rational numbers as a and b are integers but √2 is irrational numbers.

Therefore,the contradiction we suppose is wrong hence,3-√2 is irrational numbers.

Answer 2

when we subtract an irrational number from another irrational number, the difference is also irrational.