17. Show that 5-√3 is irrational.
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Let 5-√3 is a rational number
Let 5-√3=a/b (where a and b are integers)
-√3=a/b-5
5-a/b=√3
5b-a/b=√3
If LHS is rational number then its RHS is also rational number.
So √3 is a rational number.
But it is the fact that √3 is irrational number.
So our supposition/assumption is wrong.
Hence, 5-√3 is irrational number.
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