Question

Prove that 3√5 is an irrational number by contradiction method

Answer 1

Answer:

LET US ASSUME 3√5 IS AN RATIONAL NO.

SO 3√5=A/B

√5=A/3B

SINCE √5 IS IRRATIONAL AND A/3B IS RATIONAL

THEREFORE IT CONTRADICTS OUR ASSUMPTION AND OUR ASSUMPTION IS WRONG.

NOW,

3√5 IS IRRATIONAL

Answer 2

Let 3 root 5 be a rational number.

Now, as we know the quotient of two rational numbers is always a rational number.

Dividing by 3 we get

3 root 5 /3 is a rational number

root 5 is a rational number

But we know that root 5 is irrational number so our contradiction is wrong

3root 5 is irrational.

Hence proved.^_^