Question

A six-digit number pq5616 is the cube of a two-digit number 5r. Find p,q,r

pls give a detailed answer

Answer 1

Answer:

tioiyythgthgghhuyrfdeertyui

Answer 2

Answer:

For a number x to be a perfect cube and perfect square both, it has to be of form x= n6 where n may or may not be a prime number.

9^6 > 500,000 so there's no need to check beyond 9

2^6 is obviously smaller than 100,000 but we need to check for higher powers which are mulitples of 6, i.e., 12 and 18. 2^12 is smaller too, and while 2^18 falls in the perfect range, it's sum of digits is not 43.

Proceeding in a similar manner till 9^6, we find that there's no such number which has it's sum of digits equal to 43 in the given range. Please correct me if I am wrong.

499849

There is no 6 digit cube number which has sum as 43. Hence, your second statement is wrong.

Now, 6 digit Square numbers which have sum as 43 are 499849, 678976, 693889, 784996 and 786769.

As per your third condition, first number ie 499849 is the answer.