Question

(√2+√3)^2 is irrational or rational number​

Answer 1

Answer:

proved that 1+2–√ is irrational, so I will now prove that 3–√+2–√ is irrational as well.

Let’s assume by contradiction that 3–√+2–√ is rational. Therefore there exist integers a,b such that,

ab=3–√+2–√⟹

a2b2=(3–√+2–√)2=3+26–√+2⟹

26–√=a2b2−5=a2−5b2b2⟹6–√=a2−5b22b2

But we know that 6–√ is not rational, since 6 is not square (analogous to the ). So our premise that 3–√+2–√ is rational must be false. QED.

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