Question

prove that 2 minus 3 root3 are irrational number ​

Answer 1

here a, b and 2 are integers. so 2- a/b is rational. so √3 is also rational. but this contradicts the fact that √3 is irrational (as we know it is irrational).

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Answer 2

Answer:

2-3√3 = p/q , where p, q belongs to integers , q is not equal to 0.

2 - p/q = 3√3

2q - p/q = 3√3

√3 = 2q - p/ q /3

√3 = 2q - p /q (1/3)

√3 = 2q - p/3q

Therefore 2q-p/3q is rational number.

√3 is rational number

Our assumption √3 is rational number is wrong.

Therefore 2-3√3 is irrational number.

I hope it will help you mate!