Question

prove that 8-2 root 3 is irrational number​

Answer 1

Answer:

LET US ASSUME THAT 8-2ROOT3 IS AN IRRATIONAL NUMBER.

SO 8-2ROOT3=P/Q

WHERE P AND Q ARE INTEGERS..

-2ROOT3=P/Q-8

ROOT3=(P/Q-8)/-2

THUS (P/Q-8)/-2 IS A RATIONAL NO. WHERE PA ND Q ARE INTEGERS.

SO, ROOT 3 IS ALSO IRRATIONAL..

BUT THIS CONTRADICTS THE FACT THAT ROOT 3 IS IRRATIONAL.

THUS OUR ASSUMPTION WAS WRONG.

HENCE,PROVED...

PLEASE MARK IT AS THE BRAINLIEST..

Answer 2

Answer:

Let's assume that 8-2 root 3 is a rational no.

i.e. it can be written in the form of a/b where a,b are rational no. and a unequal to 0

8-2 root 3= a/b

8-a/b=2 root 3

8b-a/2b= root 3

L.H.S is rationalized so R.H.S should also be rational

but it contradicts the fact that root 3 is rational

Hence,our assumption was wrong

Therefore,8-2 root 3 is an irrational no.

Step-by-step explanation: