Question

prove 2-root 3 is irrational given that root 3 is irrational ​

Answer 1

Answer:

Hope this helps!!

.

.

..

Step-by-step explanation:

as root 3 is irrational ie given it means that the statement root 3=2p/q is false.Hence it is irrational

Answer 2

let 2-√3 be rational

so, 2-√3 = p/q where p and q are co-prime integers and q is not equal to 0

2-√3 = p/q

-√3 =p/q - 2

√3= - ( p/q -2q/q)

√3= -(p-2q/q)

√3= -p+2q/q

√3=2q-p/q

as p andq are integers, 2q-p/q is rational but we know that √3 is irrational.

So this contradiction has arrived because of our faulty assumption that 2 - √3 is rational. Hence it is irrational.

pls amrk as brainliest