Why is no isomorphism possible from $(\Bbb Q^*,\cdot)$ to $(\Bbb R^*,\cdot)?$

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Why is no isomorphism possible from $(\Bbb Q^*,\cdot)$ to $(\Bbb R^*,\cdot)?$

Is it happening for different cardinalities of the groups?Is there any reason related to homomorphism?Please help me.Thank you in advance.