Question

Show that 5-square root 3 is irrational

Answer 1

         

$Assume that \ \ 5-\sqrt{3}\ \ is rational. \\ \\ So let \ \ 5-\sqrt{3}=x.\ So that both sides are rational. \\ \\ \\ x=5-\sqrt{3} \\ \\ \sqrt{3}=5-x \\ \\ \\ Here, if both sides of \ x=5-\sqrt{3}\ \ are rational, then so will be \ 5-x=\sqrt{3}. \\ \\ But \ \sqrt{3}\ is irrational. \\ \\ Thus our assumption is contradicted. \\ \\ \\ \ \therefore\ 5-\sqrt{3}\ is irrational. \\ \\ \\ Hence proved!$

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Answer 2

Answer:

Step-by-step explanation:

Le us assume, to the contrary that 5-sq.root 3 is rational.

We take 5sq.root3 = a/b where a and b are coprime numbers

Rearranging, we get under.root3 = a/5b

Since 5,a and b are integers, a/5b is rational, and so under.root3 is rational.

But this contradicts the fact that under.root3 is irrational.

So, we conclude 5sq.root3 is irrational