Question

how to show 2/root 5 as irrational

Answer 1

to prove 2✓5 as irrational .

let 2✓5 be a rational number
2✓5=p/q. where p and q are integers.
✓5=p/2q

as we know P /2q is is a rational number show root 5 will also be a rational number but we know that root 5 is irrational number so contradiction is wrong 2✓5 will be a irrational number .



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Answer 2

let 2√5 is rational
then we can write
2√5=a/b
but 2√5 is a product of rational and irration and we now that product of rational and irrational is irrational this contradict the fact that w√5 is reason hence it is irrational
hence proved