Final answer:
The most significant statement when a patient with hypertension is prescribed a beta-blocker is their history of asthma, as beta-blockers may worsen asthma symptoms.
Step-by-step explanation:
The statement by the patient that the nurse should recognize as most significant when admitting a patient for hypertension who has been prescribed a beta-adrenergic blocker is: "I have always had problems with my asthma." Beta-blockers can exacerbate asthma symptoms because they block the beta receptors in the bronchial tubes, leading to bronchoconstriction. This is particularly relevant for patients with respiratory issues like asthma and can be contraindicated in their treatment plan.