if-a-is-a-negative-number-is-sqrt3-8-a3-a-positive-number-a-negative-number-or-not-a-real-number-exp

Question

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

Finian Lickona · Accepted Answer

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&#x27;m going to split this into theseventy constituent parts. So I&#x27;m gonna write this as a negative one coefficient, and I&#x27;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&#x27;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,

Amy Jiang · Answer

Okay, so let&#x27;s first note that will 81. That&#x27;s 32 of our four, So that gives us three.

Amy Jiang · Answer

So let&#x27;s rewrite 81 as reaching about four. I know we have the four through of a power of four, so that&#x27;s this equal to our inside term, which is three.

Amy Jiang · Answer

because some of us that we have the fourth root of our inside term, which is a negative number. So this means ads. This is not a burial number.

Amy Jiang · Answer

Okay, So if we have a is greater than zero, then that means if we write about this, are a term is positive. So if we have negative eight, that&#x27;s going to be a negative value. And we know that the square root of a negative value is not a viral number. Okay, I know for part B, if we have a is less than zero, that means that&#x27;s we have negative times. A day is negative, so negative times negative is a positive value. So this means that we have a positive value in here. Ended in negative outside, so negative times positive is a negative. So we get a negative value. And here, when a is equal to go, we have negative square roots of minus Errol. Would you like to negative square roots of salt? And that&#x27;s the secret to dough.

Amy Jiang · Answer

Okay, so we want to have always falling. So it&#x27;s no that 64 is a perfect square. That&#x27;s eight to park, too, and this year is people to it.

Problem

In $3-38$ , write each radical in simplest radica…

Problem 2 Easy Difficulty

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

Answer

The answer would be negative.

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The answer would be negative.

Algebra 2 and Trigonometry

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Ann Xavier Gantert

Algebra 2 and Trigonometry