Question

prove that 7 +root 5 is irrational number​

Answer 1

Answer:

Yes, it is an Irrational no.

Step-by-step explanation:

$7+\sqrt{5}$ Cannot be rationalised or written in the form of p/q

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Answer 2

Answer

we have to prove that 7+root5 is irrational

let us assume that

i.e. 7+root5 is rational

hence 7+root5 can be written in p/q form

where a and b(a is not equal to b) are co prime ( no common factor other than 1)

hence 7+root5 =a/b

root5=a/b-7

root5=a-7b/b

root5 is irrational and a-7b/b is rational

here, root5 is irrational

but a-7b/b is rational

since, rational not equal to irrational

this is a contraction

hence, our assumption is inncorrect

hence, proved 7+root5 is irrational