Final answer:
The square root of (-5x)^3 does not make sense for any values of x.
Step-by-step explanation:
We need to find the square root of (-5x)^3 and determine for which values of x this expression makes sense.
Let's break it down step by step:
1. To find the square root of a number or expression, we look for a number that, when multiplied by itself, equals the given number or expression. In this case, the square root of (-5x)^3 is a number or expression that, when multiplied by itself three times, equals (-5x)^3.
2. To simplify (−5x)^3, we raise −5x to the power of 3, which means multiplying it by itself three times:
(−5x)^3 = (−5x)(−5x)(−5x) = −125x^3.
3. Now, we need to find the square root of −125x^3:
√(−125x^3)
Since the square root of a negative number is not a real number, this expression does not make sense for any values of x. Therefore, there are no values of x for which this expression makes sense.