Question

Prove that root 2 is an irrational number by contradiction method.​

Answer 1

Answer:

hope this helps u.

mark braliest.

follow me

Answer 2

To prove:

Root 2 is an irrational number by contradiction method.

Proof:

Assume √2 is a rational number. It can be expresses as a/b where b≠0.

Hence,

• (√2)² = (a/b) ²
• 2 = a²/b²
• 2b² = a²... (1)

here, a² is a multiple of 2.Hence a is a multiple of 2.

• a = 2m
• a² = 4m²...(2)

Using (1) and (2)

• 2b² = 4m²
• b² = 2m²...(3)

(2) and (3) implies that both a and b have a common factor 2.

It contradicts the fact that they are co-primes. Hence, they are not rational numbers.

Hence, √2 is an irrational number.

This proves that root 2 is an irrational number.

Hence proved.

#SPJ3