Question

Prove that 7+3√2 is an irrational number , where root 2 is given to be an irrational number.

Answer 1

Step-by-step explanation:

given Root 2 is irrational....

let, assume that the num is rational

so,..

7+3root2=a/b   ( where a and b are coprime)

3root2=a-7b/b           co-prime mean HCF=1

root 2=a-7b/3b

we know that root2 is irrational

it contradicts assumsion that the number is rational...

so the number 7+3root2 is irrational...

Hence,Proved...

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