Question

Prove that 7√5 is irrational​

Answer 1

Step-by-step explanation:

let 7 root 5 is rational

a/b = 7 root 5 ( where a and b are integers and co prime )

a/ 7b = root 5

a/7b is rational a and b are integers

root 7 is irrational

rational not equal to irrational

our supposition is wrong 7 root 5 is irrational

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Answer 2

Step-by-step explanation:

• let us assume,to the contrary, that 7√5 is rational.
• that is,we can find coprime a and b (b≠o) such that
• 7√5=a/b
• By rearranging , we get
• √5=a/7b

since,a and b are integers, therefore a/7b is rational, and so √5is rational.

but this contradicts the fact that√5is irrational.

so, we conclude that 7√5 is irrational.

Answer

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