please please please help!

Question

compute the square root of the base-5 number 243331₅ and leave the answer in base 5

Answer 1

Is it OK to convert into base-10 first, then compute the root in base-10 and finally convert the result back to base-5?

 

243331₅

= 2*5⁵ + 4*5⁴ + 3*5³ + 3*5² + 3*5¹ + 1*5⁰

= 2*3125 + 4*625 + 3*125 + 3*25 + 3*5 + 1

= 6250 + 2500 + 375 + 75 + 15 + 1

= 9216

= 96²

 

96 = 3*25 + 4*20 + 1

= 3*5² + 4*5¹ + 1*5⁰

= 341₅