Question

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

and a square number.

Answer 1

Answer:

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.

Answer 2

The value 279 expressed as the sum of a power of 3 and a square number is $3^5 + 6^2$

The power of 3 of a number is expressed as a^3

The square of a number is b^2

Hence we need to find the value of a and b such that the addition will give 279.

since 3^5 = 243

279 - 243  = 36

Write 36 as a square number:

36 = 6^2

Hence the value 279 expressed as the sum of a power of 3 and a square number is $3^5 + 6^2$

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