Il est nécessaire que vous .......... le ménage. (faire)
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Verbs and expressions that indicate necessity, doubt, emotion, or will (like “il faut que,” “il est important que,” “je veux que”) require the subjunctive mood.
The expression “Il est nécessaire que” indicates a need, obligation, or emotion — which always triggers the use of the subjonctif présent in French.
We must conjugate the verb “faire” in the present subjunctive for the subject “vous.”
The present subjunctive of “faire” for “vous” is fassiez.
So the completed sentence is: Il est nécessaire que vous fassiez le ménage.
This means: “It is necessary that you do the cleaning.”