Multiplicative Group of Rationals is Normal Subgroup of Reals

Theorem
Let $$\left({\mathbb{Q}^*, \times}\right)$$ be the Multiplicative Group of Rational Numbers.

Let $$\left({\mathbb{R}^*, \times}\right)$$ be the Multiplicative Group of Real Numbers.

Then $$\left({\mathbb{Q}^*, \times}\right)$$ is a normal subgroup of $$\left({\mathbb{R}^*, \times}\right)$$.