prove that 3root2 – 2root3 is irrational Please give answer with explanation Question prove that 3root2 – 2root3 is irrationalPlease give answer with explanation in progress 0 Math Mary 10 months 2021-08-20T19:05:43+00:00 2021-08-20T19:05:43+00:00 2 Answers 0 views 0
Answers ( )
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.
when we subtract an irrational number from another irrational number, the difference is also irrational.