Question

show that the following are irrational numbers are root 3​

Answer 1

Answer:

Since both q and r are odd, we can write q=2m−1 and r=2n−1 for some m,n∈N. ... Therefore there exists no rational number r such that r2=3. Hence the root of 3 is an irrational number.

Answer 2

Answer:

Let us assume the contrary that root 3 is rational. Then √3 = p/q, where p, q are the integers i.e., p, q ∈ Z and co-primes, i.e., GCD (p,q) = 1. Here 3 is the prime number that divides p2, then 3 divides p and thus 3 is a factor of p. ... Therefore, the root of 3 is irrational.

Step-by-step explanation:

sana po makatulong