And when she was baptized - Apparently without any delay. Compare Acts 2:41; Acts 8:38. It was usual to be baptized immediately on believing.
And her household - Greek: her house ὁ οἶκος ἀυτῆς ho oikos autēs, her family. No mention is made of their having believed, and the case is one that affords a strong presumptive proof that this was an instance of household or infant baptism. Because:
(1) Her believing is particularly mentioned.
(2) It is not intimated that they believed.
(3) It is manifestly implied that they were baptized because she believed. It was the offering of her family to the Lord. It is just such an account as would now be given of a household or family that were baptized upon the faith of the parent.
If ye have judged me to be faithful - If you deem me a Christian or a believer.
And she constrained us - She urged us. This was an instance of great hospitality, and also an evidence of her desire for further instruction in the doctrines of religion.