Question

Prove that root 3 is irrational no ​

Answer 1

Answer:

1.73205080757

Step-by-step explanation:

root3=1.73205080757

we know that rational can be expressed as p/q and q=0

and it should be terminating or nonterminating

non recurring

even root3 is not perfect square

Answer 2

Answer:

Let us assume to the contrary that √3 is a rational number.

It can be expressed in the form of p/q

where p and q are co-primes and q≠ 0.

⇒ √3 = p/q

⇒ 3 = p^2/q^2 (Squaring on both the sides)

⇒ 3q^2 = p^2………………………………..(1)

It means that 3 divides p2 and also 3 divides p because each factor should appear two times for the square to exist.

So we have p = 3r

where r is some integer.

⇒ p^2 = 9r^2………………………………..(2)

from equation (1) and (2)

⇒ 3q^2 = 9r^2

⇒ q^2 = 3r^2

Where q2 is multiply of 3 and also q is multiple of 3.

Then p, q have a common factor of 3. This runs contrary to their being co-primes. Consequently, p / q is not a rational number. This demonstrates that √3 is an irrational number.