prove that 3+ 2 root 5 is irrational
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Answer:
take root 5 is ration
Step-by-step explanation:
let root 5=p/q
(root 5)2=p2/q2
5=p2/q2
p2=5q2
5 divides p2
5 divides p.
let p=5r
(5r)2=5q2
25r2=5q2
5r2=q2. ( cancel 25 and 5)
5 divides q2
5 divides q
p and q have common factor 5
so our assumption is wrong by contradiction fact root 5 is irrational
no let 3+2root5 be rational
3+2root5=p/q
2 root5=p/q-3= p-3q/q
root 5=p-3q/2q
but root 5 is irrational (proved)
p-3q/2q=integer/integer=rational
our assumption is wrong by contradiction fact 3+2root 5 is irrational
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