Question

Prove that the following numbers are irrational:
(i) 3√2
(ii) 3√3
(iii) 4√5.​

Answer 1

Answer:

1. 1.3+√2 = a/b ,where a and b are integers and b is not equal to zero .. therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers.. ... So, it concludes that 3+√2 is irrational.
2. 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.
3. Let 4 - √5 be a rational number, hence it can be expressed in the form of p/q where p&q are co-prime integers. ... Hence, 4 - √5 is irrational.

Step-by-step explanation:

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