Let us assume that 6 + v2 is a rational
number.
So it can be written in the form a/b
6+ √2=a/b
Here, a and b are coprime numbers and b≠0
6+12=a/b
By solving the equation we get,
√2=a/b-6
√2=a-6b/b
This shows a-6b/b is a rational number.
But we know that √2 is an irrational
number, it contradicts our assumption
Our assumption 6 + √2 is a rational
number is incorrect
Therefore, 6 + √2is an irrational number
Hence, it is proved that 6 + √2 is an irrational number.
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Answers & Comments
Let us assume that 6 + v2 is a rational
number.
So it can be written in the form a/b
6+ √2=a/b
Here, a and b are coprime numbers and b≠0
6+12=a/b
By solving the equation we get,
√2=a/b-6
√2=a-6b/b
This shows a-6b/b is a rational number.
But we know that √2 is an irrational
number, it contradicts our assumption
Our assumption 6 + √2 is a rational
number is incorrect
Therefore, 6 + √2is an irrational number
Hence, it is proved that 6 + √2 is an irrational number.