Show that 5-V3 is Irrational number.

1.	Show that 5-V3 is Irrational number.
Answer» Let us assume that 5 - root 3 is rational. Then it can be written in the form 5 - root3 = p/q or 5 - p/q = root3 It implies root3 is a rational number [Since 5 - p/q are rationals] But this contradicts to the fact that root 3 is irrational. Hence our supposition was wrong. Therefore 5 - root 3 is irrational.

Answer»

Let us assume that 5 - root 3 is rational. Then it can be written in the form

5 - root3 = p/q

or 5 - p/q = root3

It implies root3 is a rational number [Since 5 - p/q are rationals]

But this contradicts to the fact that root 3 is irrational. Hence our supposition was wrong. Therefore 5 - root 3 is irrational.

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