Question

prove that 1/2-root 3 is irrational

Answer 1

Step-by-step explanation:

1/2-√3

(1-2√3)/2

(1-√12)/2

we know the definition of rational numbers that is every number in the form of P by q where p and q are integers and q is not equal to zero but in this case p is equal to 1 minus under root 12 so it is not a rational number

w e k n o w the numbers which are not rational and where numbers are coprime that means they have HCF as 1 are called irrational numbers so it is a irrational number

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Answer 2

let us assume that root 3 is rational ,

then it will be in the form p/q

root 3 = p/q

square both sides

3 = p square / q square

p square = 3 q square

let p be 3 r

3r square = 3 q square

9r square = 3 q square

3 r square = q square

to be a rational no it should not have any common factor other than 1 and itself

therefore root 3 is irrational

1/2 - root 3

lets assume it is rational

1/2- root 3 = p/q

- root 3 = 2 p/q

we have proved that root 3 is irrational , as it is equal to 2 p/q

therefore , 1/2-root3 is irrational

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