Their ages are:

>! $71, 9, 4$

Reasoning:

>!The oldest grandchild's age is (presumably) a perfect square, and the square of her age is $10$ years older than a reasonable grandma age, so we can guess that she is now $9$. That makes the grandma $71$, and the younger child is $4$. So thus the grandma was $64$ when she was diagnosed.