Given that , calculate without a…

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

Given that

55555^2 = 3086358025

, calculate

55556^2

without a calculator. (1) Are

3^8

and

2^6

perfect squares? (2) Find the prime factorization of

3^8 - 2^6

. Challenge: See if you can do it in your head!