Question

show that 8-2√5 is irrational given that √5 is irrational​

Answer 1

Let 8 - 2 root 5 be a rational number

8 - 2 root 5 = p/q , ( p, q ) = 1

q is not equals to 0

2 root 5 = p/q +8

2 root 5 = p+8q / q

p+8q /q is a ratinsl no.

Thetefore, 2 root 5 is also rational no.

But we know that

root 5 is irrational no.

So , there comes contradiction .

Therefore , our supposition is wrong .

8-2 root 5 is irratinal no.