Question

What is the value of z?



3
√
z
−
8
=
√
z

4


9


16


25

Answer 1

I’m not sure how to read the radical: it could mean any of these three equations. I’ll give the answers for each interpretation.

1) If 3·√(z − 8) = √z:
- Square both sides: 9(z − 8) = z → 9z − 72 = z → 8z = 72 → z = 9. (Check: z ≥ 8 OK.)

2) If 3√z − 8 = √z (i.e. 3·√z − 8 = √z):
- 2√z = 8 → √z = 4 → z = 16.

3) If ³√(z − 8) = √z (cube root of z−8 equals √z):
- Let t = √z ≥ 0. Then t^3 − t^2 + 8 = 0, which has no solution among t = 2,3,4,5 (so none of the given choices).

If you tell me which formatting is intended, I’ll confirm the single correct choice.