Question

Prove that √3+√7 is irrational.​

Answer 1

let it be rational

means it is of form x/y where x and y are co prime integers and y not equal to 0

Squaring both sides....

but it contradict the fact that x and y are co prime integers as root21 is irrational and x^2-10y^2/2y^2 is rational

this means our supposition is wrong

thus root3+root7 is irrational

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Answer 2

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Let's start

QUESTION - Prove root 3+ root 7 is irrational

Answer

We have to prove that root 3+ root is irrational.

Let us assume the opposite, that root 3+ Root 7 is rational.

Hence root 3+ root 7 can be written in the form a/b where a and b are co-prime and b not = 0

Hence

Root 3+ root 7= a/b

Root 3= a/b-root 7

Root 3= a- b root 7/b

But as we know

Root 3 is irrational

It contradicts our assumption that

Root 3+ root 7= rational number

Hence proved