prove that 2-3root 5 is irrational
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Letx=2-3√5 be a rational number.
3√5=2-x
√5 = 2 -x/3
Since x is rational, 2-x is rational and hence 2-x/3 is also rational number
→ √5 is a rational numbers, which is a contradiction.
Hence 2-3√5 must be an irrational number.
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