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Prove 3 + √5is irrational |
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Answer» Let us suppose 3+root 5 is rational.=>3+root 5 is in the form of p/q where p and q are integers and q is not =0=>root5=p/q-3=>root 5=p-3q/qas p, q and 3 are integers p-3q/3 is a rational number.=>root 5 is a rational number.but we know that root 5 is an irrational number.this is an contradiction.this contradiction has arisen because of our wrong assumption that 3+root 5 is a rational number.hence 3+ root 5 is an irrational number. |
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