prove that 2+3 root 2 is irrational number
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Assume to reach the contradiction that 2+3√2 is a rational number.
Let x = 2+3√2, where x is a rational number which values the RHS.
Consider the last line.
→ In the LHS,
⇒ x is rational.
⇒ As a rational number subtracted by another rational number gives rational number, x - 2 is rational.
⇒ As a rational number divided by another rational number gives rational number, (x - 2)/3 is rational.
Thus the LHS is rational. While the RHS √2 is irrational.
Hence this final step creates a contradiction.
Thus proved!!!
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