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In $3-10,$ tell whether each represents a number that is rational, irrational, or neither.$$\sqrt[3]{-8}$$

rational

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Chapter 3

REAL NUMBERS AND RADICALS

Section 2

Roots and Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $3-10,$ tell whether ea…

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Determine whether each exp…

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Tell whether each square r…

All right, you guys. So in this problem, we're given the cube root of negative eight and were asked to determine if this value is a rational number, an irrational number or neither. And so for us, let's try to find a factory ization kind of or simplifies cube root of negative eight. So let's start out. So we know that the cube root of negative age can also be written as the cube root of negative for times two. Or let's write a better. It could be written as a product of four times negative, too. And we just got this cause we know that four times they give to his negative eight just a simple algebraic step. We also know that four is equal to negative two times negative, too, so we can rewrite that last step as the product of negative to have donated to the negative, too. And the next step is we can rewrite this product of three negative twos as negative too cubed. And when you take the cube root of Thumping Cube, you're just going to get that something. And so the cube root of negative to cubed is just negative, too, so your route of negative eight. Simplified is going to equal negative. Too. Negative too, by definition is a rational number. So cube root negative eight is a rational value. Thank you for listening, guys. And I hope this helps. This was a pretty simple, straightforward problem. Then I hope I clear any doubts you guys head on.

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