Question

Show that Negative of an irrational number is irrational.

Answer 1

Let us assume that x is an irrational number such that - x is rational.

So, - x = `"a"/"b"` where a, b are integer and b ≠ 0

x = `"- a"/"b"`

Since, - a, b is also integer and b ≠ 0.

So x is a rational number it contradict our assumption.

∴ - x is irrational.