Ideal of Ring is Contained in Radical

Theorem
Let $A$ be a commutative ring with unity.

Let $\mathfrak a \subseteq A$ be an ideal.

Then $\mathfrak a$ is contained in its radical:
 * $\mathfrak a \subseteq \operatorname{Rad} \left({\mathfrak a}\right)$

Proof
Let $a \in \mathfrak a$.

By definition of power:
 * $a^1 = a$

Thus:
 * $a \in \operatorname{Rad} \left({\mathfrak a}\right)$