Question

prove that root 12 and 5 is the irrational number​

Answer 1

Answer:

*Hope It Helps Mark Brainliest!!!*

Step-by-step explanation:

Yes, 12−−√=23–√12=23 is irrational. There is a simple proof for the irrationality of 3–√3.

There is also a simple general proof that shows that the square root of any non-negative integer which is not a perfect square is in fact irrational. So: The square root of an integer is either an integer or it is an irrational number, it can never be a non-integer rational number.

Let’s try to prove this via proof by contradiction.

Let n∈Nn∈N, and let nn not be the square of an integer.

Assume n−−√n is rational:

n−−√=pqn=pq

with pp and qq non-negative integers, q>0q>0 and pp and qq being co-prime, i.e. gcd(p,q)=1gcd(p,q)=1.

Then

n=p2q2n=p2q2

As p2p2 and q2q2 still cannot share a common factor, q2q2 and therefore qq has to be 11, otherwise the fully-reduced fraction cannot be an integer.

Therefore

n=p2n=p2

But we assumed 

Answer 2

$\bold{\sqrt{12}=2\sqrt{3}}$ is irrational. Because of the

irrationality of $\bold{\sqrt{3}}$