NCERT Figure it Out 3 - Digital roots - Number Play
Question: (1) Digital root of an 8-digit number is 5. What is the digital root of that number plus 10? (2) Digital roots when repeatedly adding 11? (3) Digital root of 9a+36b+13? (4) Relate digital root to parity and to remainders mod 3 and 9.
Answer: (1) 6 (2) +2 pattern mod 9 (3) 4 (4) no parity rule; digital root encodes rem mod 3 and 9.
Full step-by-step NCERT solution with diagrams on Something by Zero.