1.

Prous that at 2+5√3 is an irrational number given that 3 is an irrational number​

Answer»

Let us suppose that 2+5root3 is rational.

Then,

2+5root3-2 should also be rational.[Rational-Rational=Rational]

So,

Let us now suppose that 5root3 is rational

Then,

5root3÷5 should also be rational.[Rational÷Rational=Rational]

So, ROOT 3 is rational.

But it is given that root 3 is IRRATIONAL.[If 3 is irrational, then root 3 should also be irrational.]

This is a contradiction created because of our assumption that 2+5root3 is rational.

So, we are FORCED to CONCLUDE that 2+5root3 is irrational.

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