prove that 3+ 5 root2 is an irrational number, given that root 2 is an irrational number.
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(Assumed) They must be in the form of p/q where q≠0, and p & q are co prime. ... And, Rational ≠ Irrational. Therefore we contradict the statement that, 5+3√2 is rational. Hence proved that 5 + 3√2 is irrational.
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