Question

Prove that 5+3 root2 is an irrational number

Answer 1

let 5+3 root2 is an Rational number in the form of P/q.

5+3 root2 = p/q

3 root2 = p-5q/q

root2 = p- 5q/q

But we Know that root2 is irrational number...

By this Contradiction it is proved that 5+3 root2 is an irrational number.

Hope its Helpful for you....

Answer 2

Answer:

Step-by-step explanation:

Let us assume that 5+3root2 is rational

5+3=pbyq where q is not equal to zero p, ware integers and co-primes

3root2=pbyq-5

3root2=p-5qbyq

root2=p-5qby3q

we know that ,

root2 is irrational and p-5qby3q is rational

we got,

Qbar=Q which is incorrect

This is our wrong assumption that 5+3root2 is rational

Therefore,

5+3root2 is irrational.