Question

prove that 2√3 is an irrational number​

Answer 1

Step-by-step explanation:

Proof

Let us assume that 2+√3 is a rational number.

A rational number can be written in the form of p/q.

2+√3=p/q

√3=p/q-2

√3=(p-2q)/q

p,q are integers then (p-2q)/q is a rational number.

But this contradicts the fact that √3 is an irrational number.

So,our assumption is false.

Therefore,2+√3 is an irrational number.

Hence proved.

Answer 2

Answer:

Okay

Step-by-step explanation:

We can prove this, by contraction method

So let 2 √3 is a rational number

2√3=p/q

√3 = p/2q ......................(1)

Therefore Now , p/q is a rational then p/2q is also rational number.

Then √3 is a rational number..........(2)

But it contradicts ,the fact that ,√3 is an irrational number.

therefore,√3≠ p/2q

We can say that our assumption is wrong.

( Hence proved ,2√3 is an irrational number)

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