Question

prove that√3 is an irrational number​

Answer 1

Step-by-step explanation:

see in books

you can see there

Answer 2

Step-by-step explanation:

Proof : If possible let √3 is rational

then √3 = P/q where p & q are integers & q is not equal to 0

also, p & q are co - prines

now, √3 = p/q

( square both sides)

you get,

3 = p2/q2

3q2 = p2 ----(equation 1)

also 3 divides p2

=) 3 divides p

let p= 3r gor some integer

putting p = 3r (in equation 1)

we get,

3q2 = (3r)2

3q2 = 9r2

=} q2= 3r2

3 divides q2

3 divides q

this contradicts that P & q are co - primes

these contradiction arises due to our supposition that √ 3 is rational.

therefore, our supposition is wrong

Hence √ 3 is irrational.

....Hence proved

hope this helps you