Question

The picture is the qeustion

Answer 1

n=64

Explanation:

Let think algebracially. One of the terms in the set is a fraction. A natural number must be a whole number so this means that

n must be a multiple of 8.

*N must be a multiple of 8.

Look at the third term, we know that a square root must produce a perfect square term to get a natural number. So n must be a multiple of 8 that makes the radical a perfect square

Perfect squares are.

0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225, 256, 289

N has to compute a sum greater than 225 so the perfect squares we look at must be greater than 225.

The next one is 256 but

`256 - 225 = 31`

`31 / 8 = (31)/(8)`

which isn't rational so 256 won't work. Let try 289

`289 - 225 = 64`

`64 / 8 = 8`

and

`33 + 64 = 97`

So 64 works. 64 is the answer

n=64