Answer:
n=64
Step-by-step 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
[tex]256 - 225 = 31[/tex]
[tex]31 \div 8 = \frac{31}{8} [/tex]
which isn't rational so 256 won't work. Let try 289
[tex]289 - 225 = 64[/tex]
[tex]64 \div 8 = 8[/tex]
and
[tex]33 + 64 = 97[/tex]
So 64 works. 64 is the answer
n=64
