Question

if $x^3 = -27$, then $x$ equals
-3
+3 and -3
+9 and -9
-9

Explanation:

Step1: Recall cube root definition

To solve \( x^3 = -27 \), we find the cube root of \(-27\). The cube root of a number \( a \) is a number \( x \) such that \( x^3 = a \).

Step2: Calculate cube root of -27

We know that \((-3)^3 = (-3) \times (-3) \times (-3) = -27\). Also, for real numbers, the cube root of a negative number is negative (unlike square roots, where we consider positive roots for non - negative radicands in real numbers, but cube roots have a unique real root for any real number). So \( x=-3 \).

Answer:

-3