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If $a$ is a negative number, is $-\sqrt[3]{-8 a^{3}}$ a positive number, a negative number, or not a realnumber? Explain your answer. oning Skills.

The answer would be negative.

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Chapter 3

REAL NUMBERS AND RADICALS

Section 3

Simplifying Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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find the indicated root, o…

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Consider the expression $-…

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Find each square root. If …

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All right. So in this exercise, we want to explore if the quantity negative cube root of negative eight a cube is a negative number, Positive number or not even a real number, given the fact that a is a negative number. All right, so to begin with, I'm going to split this into theseventy constituent parts. So I'm gonna write this as a negative one coefficient, and I'm going to write Ah, the radical of negative eight times the radical of a cube. So if a is a negative number, that means that a cube is also a negative numbers. So if we take the cube root of a negative number, we also get a negative number now. So this whole quantity right here is negative. And now we're going to take the cube root of negative eight. If you do, that calculation in the value is negative too. So this number is also negative. So if we multiply these two quantities together, we get a positive number because a negative number of times negative numbers a positive. However, we have this negative one coefficients. So this which is this whole quantity back to a negative number. So this entire expression, which is the expanded form of this expression, is a negative number. Okay,

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