Question

The picture is the qeustion

Answer 1

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

$256 - 225 = 31$

$31 \div 8 = \frac{31}{8}$

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

$289 - 225 = 64$

$64 \div 8 = 8$

and

$33 + 64 = 97$

So 64 works. 64 is the answer

n=64