It follows the princess confirming in March that pre-cancerous cells had been found following abdominal surgery and that she would have to undergo a course of preventative chemotherapy.
During his visit to the school, the Prince of Wales met with 10-year-old Ruby Davies, who won the solo recitation at this year’s Urdd Eisteddfod, an annual cultural festival.
She told the PA news agency she felt “amazing” after meeting the prince and that it was something she would “treasure forever”.
Prince William said he had watched the video of her performance “a few times” and said it was “very impressive”.
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“You’re going to have to teach me how to speak Welsh,” he added.
Lynne Davies, her mother, said she was happy to hear the Princess of Wales had completed chemotherapy.
The prince told one well-wisher, 74-year-old Pauline Thomas, that it was “good news” but that there was “still a long way to go”, The Sun reported.
Later on Tuesday, William visited the headquarters of the Wales Air Ambulance.
The day ended at Parc y Scarlets, home of the Scarlets rugby union team, to celebrate the contribution of current and former Welsh female rugby players.
The prince will find out more about the Welsh Rugby Union’s missing caps campaign ahead of the 2025 Women’s World Cup.
The campaign’s aim is to recognise players who missed out on caps when they played for Wales.