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

Question

prove that 3root2 – 2root3 is irrational

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10 months 2021-08-20T19:05:43+00:00 2 Answers 0 views 0

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.

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