Question

prove that 2 + 3√5 is irrational number​

Answer 1

Answer:

Step-by-step explanation:

so, assume that 2+3root 5 is rational.

2+3root5=p/q,where p and q are coprimes and q not equals to 0.

3root 5=p/q-2.

root 5=p/q-2/3.

A rational number never equals to an irrational number.

We assume that p and q are coprimes and q not equals to 0.

so, our assumption is wrong.

2+3root 5 is an irrational number.

Answer 2

Assume 2-3√5 be a rational no

therefore 2-3√5=a/b

hence √5=a-2b/3b

therefore a-2b/3b is a rational no

therefore √5 is a rational no

but we know that √5 is a irrational no

therefore our assumption was wrong that 2-3√5 is a rational no

therefore 2-3√5 is a irrational no