Question

Prove that 3-2√3 is irrational.

Answer 1

3/2√3

=√9/√12

=√(9/12)

=√(3/4)

=√3/2

√3/2 is irrational therefore 3/2√3 is irrational

Thus proven,

Answer 2

let 3 - 2√3 be rational number.

3 - 2√3 = p/q

3 - p/q = 2√3

3q - p/q = 2√3

3q-p/2q = √3

we know that the When we divide two rational number then it is rational but here it is irrational, √3

So, our assumption is wrong.

3 - 2√3 is an irrational number .

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