Fewpal
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Show that 4 - 5√2 is an irrational number.

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Solution:
Let us assume, to the contrary that
4 - 5√2 is rational.
So, we can find coprime integers a and b( 0)
such that 4 - 5√2 = a/b
=> 5√2 = 4 - a/b

=> √2 = (4b - a)/5b
Since a and b are integers, (4b - a)/5b is rational.
So,  √2 is rational.
But this contradicts the fact that √2 is irrational.
Hence, 4 - 5√2  is irrational.

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