Question

Show that 5 – √3 is irrational.

Answer 1

To prove: 5-√3 is irrational

proof:
Let us assume that 5-√3 is rational.

Let,
5– √3 = r, where 'r' is rational
5-r = √3

Here,
LHS is purely rational but on the other hand RHS is irrational
This leads to a contradiction.
Hence 5 – √3 is irrational.

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