Question

if x is rational and root y irrational prove that X + root Y is rational

Answer 1

Answer:

Step-by-step explanation:

Let us assume to the contrary that x+√y is rational

So x+√y can be written in the form a/b,where a and b are co-primes and b not equal to 0

x+√y=a/b

√y=a/b-x

√y=a-bx/b

Since x,a,b are all integers, therefore they are rational

But this contradicts the fact that√y is irrational

Hence our assumption is incorrect.

Therefore x+√y is irrational.

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