Choose two irrational numbers whose difference is a rational number. 2 −−√ , 3
–√ 7–√ , 2
–√ 5–√ , 7
2–√ , 2–√
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Answer:Euclid's proof starts with the assumption that √2 is equal to a rational number p/q.
√2=p/q. Squaring both sides,
2=p²/q² The equation can be rewritten as.
2q²=p² From this equation, we know p² must be even (since it is 2 multiplied by some number). ...
2q²=p²=(2m)²=4m² or. ...
q²=2m² ...
√2=p/q=2m/2n. ...
√2=m/n.
Step-by-step explanation:
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