Question

Prove that the following are irrationals: 7+ √5​

Answer 1

Step-by-step explanation:

Let’s assume that 7-root5 is rational, then

7 - root5 = a/b where a and b are integers.

subtracting 7 from both sides

a/b - 7 = - root 5

Multiplying both sides by -1

7 - a/b = root5

(7b - a)/b = root 5

But 7b - a is an integer and b is an integer, so root5 is rational contradicting the assumption.