prove that please help me
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above is the pic
Step-by-step explanation:
I hop it's help
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Step-by-step explanation:
The following proof is a proof by contradiction.
Let us assume that √6 is rational number.
Then it can be represented as fraction of two integers.
Let the lowest terms representation be:
√6 = a/b
Note that this representation is in lowest terms and hence, a and b have no common factors
a ² =6b²
From above a ² is even. If a² is even, then a should also be even.
⟹a=2c
4c² = 6b²
2c²=3b²
From above 3b² is even. If 3b² is even, then b² should also be even and again b is even.
But a and b were in lowest form and both cannot be even. Hence, assumption was wrong and hence,
6
is an irrational number.
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