Question

what is the cube root of 1,000?
\sqrt3{1,000} = 10
paige says -10 is also a cube root of 1,000. is she correct?
yes, because (-10)^3 = 1,000.
no, because (-10)^3 = -1,000.

Explanation:

To determine if \(-10\) is a cube root of \(1000\), we calculate \((-10)^3\). Using the rule of exponents for negative numbers, \((-a)^3=-a^3\) when \(a\) is a real number. So \((-10)^3 = (-10)\times(-10)\times(-10)\). First, \((-10)\times(-10) = 100\), then \(100\times(-10)=-1000\). Since \((-10)^3=-1000
eq1000\), Paige is incorrect. The correct option is the one stating "No, because \((-10)^3 = -1000\)".

Answer:

B. No, because \((-10)^3 = -1,000\) (assuming the second option is labeled B, as the first is about a wrong calculation and the second is correct in showing \((-10)^3\) equals \(-1000\) not \(1000\))