tatemthompson123
Answered

What is the following quotient?

[tex]\[
\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}
\][/tex]

A. [tex]\(2(\sqrt[3]{3}) - \sqrt[3]{18}\)[/tex]

B. [tex]\(2(\sqrt[3]{3}) - 3(\sqrt[3]{2})\)[/tex]

C. [tex]\(3(\sqrt[3]{3}) - \sqrt[3]{18}\)[/tex]

D. [tex]\(3(\sqrt{3}) - 3(\sqrt{2})\)[/tex]



Answer :

GinnyAnswer
To solve this problem, we need to calculate and compare the given expressions step-by-step. Let's go through each part of the question in detail.

1. Compute the quotient:
[tex]\[ \frac{6 - 3(\sqrt[3]{6})}{\sqrt[3]{9}} \][/tex]

Numerator: [tex]\( 6 - 3(\sqrt[3]{6}) \)[/tex]

Denominator: [tex]\( \sqrt[3]{9} \)[/tex]

Numerical result: [tex]\( 0.26375774640592026 \)[/tex]

2. Calculate each of the choices:

- Choice 1: [tex]\( 2(\sqrt[3]{3}) - \sqrt[3]{18} \)[/tex]

Numerical result: [tex]\( 0.2637577464059202 \)[/tex]

- Choice 2: [tex]\( 2(\sqrt[3]{3}) - 3(\sqrt[3]{2}) \)[/tex]

Numerical result: [tex]\( -0.8952640090698027 \)[/tex]

- Choice 3: [tex]\( 3(\sqrt[3]{3}) - \sqrt[3]{18} \)[/tex]

Numerical result: [tex]\( 1.706007316713328 \)[/tex]

- Choice 4: [tex]\( 3(\sqrt{3}) - 3(\sqrt{2}) \)[/tex]

Numerical result: [tex]\( 0.9535117355873464 \)[/tex]

From these calculations, we can see that the quotient [tex]\( \frac{6 - 3(\sqrt[3]{6})}{\sqrt[3]{9}} \)[/tex] (which is approximately [tex]\( 0.26375774640592026 \)[/tex]) closely matches the value of Choice 1: [tex]\( 2(\sqrt[3]{3}) - \sqrt[3]{18} \)[/tex] (which is approximately [tex]\( 0.2637577464059202 \)[/tex]).

Therefore, the correct answer is:

[tex]\[ 2(\sqrt[3]{3}) - \sqrt[3]{18} \][/tex]

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