Question

Prove that 5 + √7 is irrational​

Answer 1

Answer:

We all know that √7 is irrational

Let us assume to the contrary that 5+√7 is rational

So,it can be written in the form a/b where a and b are co-primes,and b not equal to zero.

5+√7=a/b

√7=a-5b/b

Since a,b and 5 are integers, therefore the are rational

But this contradicts the fact that√7 is irrational

Hence our assumption is incorrect

Therefore 5+√7 is irrational

Explanation:

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Answer 2

Explanation:

lets assume for the contrary that 5+√7 is rational so that means it can be written in the form p/q where p and q can have factors other than 1 and themselves and can be divisible so, we can write that,

5+√7=a/b , where a and b are two co primes and factors of 5+√7

now ,

√7=a-5b/b

so as a-5b/b is rational then√7 is rational but, it contradicts the fact that √7 is irrational.

so that implies that our assumption is wrong.

so 5+√7 is irrational