Two numbers, a and b, are in the golden ratio if:
a/b = (a+b) / a
where a is the larger number (a > b). You are given that b = 8, so:
a / 8 = (a + 8) / a
Cross multiply:
a2 = 8·(a + 8)
a2 = 8a + 64
a2 - 8a - 64 = 0
Solve using the Quadratic Formula. Remember to simplify the radical. You'll get two answers. One of the answers is greater than b (b=8), the other is not. Use your calculator to estimate the values of the two answers. The one that is greater than b is the answer, but leave it in simplified radical form.
