Show that 279 can be expressed as the sum of a power of 3

and a square number.

279 = 3^5 + 6^2

Step-by-step explanation:

The highest power of 3 that 279 can be expressed is 5

3 raise to the power of 5 is 243

The difference between 279 and 243 is 36

The square root of 36 is 6

Therefore, 279 is the sum of 3 raise to the power of 5 and the square of 6.

3^5 + 6²

Step-by-step explanation:

To get the answer we will try a certain method known as the trial amd error method.

Here, we will list the various multiples of 3 and also a square whose addition with the power of 3 will yield the desired answer which is 279.

The list below contains the power of 3:

3^1=3

3^2=9

3^3=27

3^4=81

3^5=243

3^6=729 (not applicable because it has already surpassed the number 279)

From here we subtract the above "powers" from 279 starting from the largest which is 3^5.

279-243=36

Here, 36 is a perfect square and now we need to find the square root which is√36 = 6

Therefore, 3^5 + 6² = 279