Can I still pray after having intercourse even after doing wudu? I am a married man but not sure if I require a full shower/bath.
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— An-Nisa 43 —
O you who have believed, do not approach prayer while you are intoxicated until you know what you are saying or in a state of janabah, except those passing through [a place of prayer], until you have washed [your whole body]. And if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and find no water, then seek clean earth and wipe over your faces and your hands [with it]. Indeed, Allah is ever Pardoning and Forgiving.
Sexual intercourse, or ejaculation without intercourse, puts the body in a state of janabah. Ghusl (the full body bath) is necessary before prayer unless water is unavailable, in which case tayammum (the dry ablution) would be acceptable. Wudu would be insufficient in this case.
However, if no actual sexual intercourse occurred (e.g. limited to kissing, holding, etc) and no ejaculation occurred, wudu would suffice.
What you're talking about needs some more information. After intercourse, in Islam its necessary for you and partner to take bath; Ghusl. Along with Ghusl you can have ablution. That's required. And after this. You can go for your prayers.
Yes, you require a full shower/bath. Intercourse is not an issue. How to cleanse yourself is. You need to fully clean yourself, that can be done by taking shower!
Intercourse/sex (anything involving the actual sex act and/or ejaculation) means you are in a state of Janabah and thus requires Ghusl. Only after removing that state of Janabah by making Ghusl you can make Wudu for prayer.
Only in exceptional cases (when prayer time is nearly ended) Wudu might be temporarily for (that specific) prayer ok.