How to show 268 as a sum of a power of 3 and a square number
Accepted Solution
A:
Answer:[tex]\large\boxed{268=3^5+5^2}[/tex]Step-by-step explanation:Consecutive power of number 3:[tex]3^1=3\\3^2=9\\3^3=27\\3^4=81\\3^5=243\\3^6=729>268[/tex][tex]268-243=25=5^2[/tex]Therefore[tex]268=243+25=3^5+5^2[/tex]Let's check the others:[tex]268-81=187\leftarrow\text{it's not a square}\\\\268-27=241\leftarrow\text{it's not a square}\\\\268-9=259\leftarrow\text{it's not a square}\\\\268-3=265\leftarrow\text{it's not a square}\\\\[/tex]Therefore we have only one solution.