Question

prove that (5+2√2)whole square is an irrational number...????
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Answer 1

To Prove: (5 + 2√2)^2 ∈ P.

Proof:

By expanding (5 + 2√2)^2, we get 33 + 20√2.

Assume that (33 + 20√2) can be expressed in form of p/q where p and q are integers and q ≠ 0.

So,

p/q = 33 + 20√2

⇒ p/q - 33 = 20√2

⇒ (p - 33q)/q = 20√2

⇒ √2 = (p - 33q)/20q

This means √2 is a rational number. But it's a fact that √2 is an irrational number. Thus, we reached at a contradiction. Or, (5 + 2√2)^2 is an irrational number.