Question

prove that 2-√3 is an irrational
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Answer 1

Hi mate..

Let us assume tht 2- root 3 is rational..whereas a/b^2 is nt equal to 0..

Therefore 2-root 3 = a/b^2 ------> 1

2+a^2/b^2= root 3

2b+a/b = root 3

Here 2b+a /b is rational and root 3 is irrational hence our assumption is wrong and 2-root 3 is irration..

Hence proved..

Hope it may help u plz mark as brainlist..

Answer 2

Answer:

Step-by-step explanation:

Let us assume that 2-√3 is rational.

so it can be written of form a/b (b≠0) where both a and b are co-primes

so, 2-√3 = a/b

⇒ √3 = 2- a/b

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).

this contradiction has rise due to our wrong assumption of 2-√3 as rational.

 hence, it is irrational.

Hope this will help you.