Question

prove 5+2√7 is irrational number​

Answer 1

Answer:

Let, 5+2√7 be rational.

Therefore, 5+2√7 =a/b where a and b are integers having no common factors other than 1.

Now, 5+2√7=a/b

=>2√7=a/b-5

=>2√7=a-5b/b

=>√7=a-5b/2b

Since, a and b are integers, therefore, √7 is rational. This contradicts the fact that √7 is irrational. Therefore, our assumption was wrong. Hence, 5+2√7 is irrational.

Answer 2

Answer:

Let, 5+2√7 be rational. Therefore, 5+2√7 =a/b where a and b are integers having no common factors other than

1. Since, a and b are integers, therefore, √7 is rational.

This contradicts the fact that √7 is irrational.

Let 5+2√7 be a rational no.

therefore 5+2√7=p/q

2√7=p/q-5

2√7=p-5q/q

√7=p-5q/2q

therfore p-5q/2q ia a rational no.

therefore √7 is also a rational number

but it is not possible as root 7 is an irrational no. therefore our assumption is wrong

thanks