Question

Given that √5 is an irrational number, prove that
(5+2√3) is an irrational no.​

Answer 1

Answer:

(5+2√3) is an irrational number.

Step-by-step explanation:

Let us assume to the contrary, that (5+2√3) is a rational number.

That is , a and b are integers and b is not equal to 0

5+2√3 = a

b

5 - a = - 5 - 2√3

b

5b - a = - 5 - 2√3

b

Since, a and b are integers, 5b - a is a rational number so

b

- 5 - 2√3 is also rational number.

But it is given that √3 is an irrational number

Therefore, (5+2√3) is an irrational number.

Hope it helps you....