Math, asked by swapnaritam, 9 months ago

Prove 2-√3 as an irrational no. Please do all the steps​

Answers

Answered by adityabhatnagar155
3

Answer:

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Answered by yogeshkumar6107
3

Answer:

let 2-√3 is a rational number

squaring the term

(2-√3)^2 = 4 + 3 - 4√3 is a rational number

{(a-b)^2 = a^2 + b^2 -2 ab}

(2-√3)^2 = 7 - 2√3 is a rational

but (2 - √3)^2 being the sum of a rational and an irrational is irrational.

thus, we arrive at a contradiction .

this contradiction arises by assuming that (2-√3) is rational.

so, (2-√3) is irrational.

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