Question

How to show 268 as a sum of a power of 3 and a square number

Answer 1

Answer:

$\large\boxed{268=3^5+5^2}$

Step-by-step explanation:

Consecutive power of number 3:

$3^1=3\\3^2=9\\3^3=27\\3^4=81\\3^5=243\\3^6=729>268$

$268-243=25=5^2$

Therefore

$268=243+25=3^5+5^2$

Let's check the others:

$268-81=187\leftarrow\text{it's not a square}\\\\268-27=241\leftarrow\text{it's not a square}\\\\268-9=259\leftarrow\text{it's not a square}\\\\268-3=265\leftarrow\text{it's not a square}$

Therefore we have only one solution.

Answer 2

Answer:

So 268 = 3^x + n^2.

Use trial and error. We know 25 + 243 = 268 so 5^2 + 3^5

Step-by-step explanation: