Question

prove that 1 by 2 + root 3 is an irrational number ​

Answer 1

1/2 + _/3


Let 1 / 2+ _/ 3 is an rational no.

1/2+_/3 = p/ q where p and q both are co - prime

Now ;

1/ 2 + _/3 = p/ q

q / 2 + _/3 = p


q = 2p + _/3 p


•°•Our Contradiction is wrong becoz irrational never = rational no.

•°•1/ 2 + _/3 is an irrational no.

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Answer 2

Answer:

1/2+√3 is irrational

Step-by-step explanation:

Let us assume to the contrary that 1/2+√3 is rational

We find coprime a&b such that

1/2+√3=a/b

I.e. √3 = (2a-b)/2b

As a and b are rational integers, √3 is also a rational no.

But this contradicts the fact that √3 is irrational.

Thus,. Our assumption was wrong.

Hence, PROVED (1/2+√3) IS IRRATIONAL.