Let \(R\) be a commutative ring and \(I\) an ideal of \(R\), and let \(\sqrt{I} =\{a \in R |a^m \in I \) for some positive integer \(m\}\) Show that
(i) \(\sqrt{I}\) is an ideal of \(R\) and \(I \subseteq \sqrt{I}\) ,
(ii) \(\sqrt{\sqrt{I}}=\sqrt{I}\) ,
(iii) If \(R\) is with identity and \(\sqrt{I} =R\), then \(I=R\) . What is \(\sqrt{I}\), when \(I=\{0\}\). (\(\sqrt{I}\) is called the radical of \(I\)).
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