The First Math Problem

Show that sqrt(6)+sqrt(3) is irrational.

Proof:

Imagine sqrt(6)+sqrt(3) is rational,

Let p/q=sqrt(6)+sqrt(3), p and q are natural numbers and (p,q)=1,

Then p^2=3*(3+2*sqrt(2))*q^2,

Thus 3|p,

Let p=3m,

Then 3m^2=(3+2*sqrt(2))*q^2,

Thus 3|q, which contradicts our initail condition (p,q)=1,

Hence sqrt(6)+sqrt(3) is irrational.

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