Math, asked by Srinjoydora, 1 year ago

Prove that 2 - root 3 is irrational

Answers

Answered by Anonymous
69
Let 2-√3 be rational

2-√3=p/q

√3=p/q+2

√3=(p+2q)/q(Integer/Integer)

√3 is a irrational number

it shows our supposition was wrong

hence 2-√3 is a irrational number
hope it helps u

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Answered by parmesanchilliwack
33

Answer:

Here, the given number is,

2 - √3

Let us assume that 2 - √3 is a rational number,

Then by the property of rational number,

2-\sqrt{3}=\frac{p}{q}

Where, both p and q are integers, q ≠ 0,

\implies \sqrt{3}=2-\frac{p}{q}

\implies \sqrt{3}=\frac{2-p}{q}

Since, p and q are integers,

⇒ 2 - p and q are integers,

\frac{2-p}{q} is a rational number such that q ≠ 0

But we know that √3 is an irrational number,

And, we can not equate a rational number and an irrational number,

Therefore, our assumption is wrong, 2 - √3 is not a rational number,

⇒ 2 - √3 is an irrational number.

Hence, Proved.

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