Math, asked by laxmiperugu69, 8 months ago

prove that 3+ 2 root 5 is irrational
prove \: 3 +2 \sqrt{5}  \: is \: irrational

Answers

Answered by adithyakrishnan1888
0

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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