Answered

Select the correct answer.

Which expression is equivalent to [tex]5 \sqrt[3]{6c} + 7 \sqrt[3]{6c}[/tex], if [tex]c \neq 0[/tex]?

A. [tex]35 \sqrt[3]{6c}[/tex]
B. [tex]12 \sqrt[3]{12c}[/tex]
C. [tex]12 \sqrt[3]{6c}[/tex]
D. [tex]72c[/tex]



Answer :

To determine which expression is equivalent to [tex]\(5 \sqrt[3]{6c} + 7 \sqrt[3]{6c}\)[/tex], we need to follow these steps:

1. Identify like terms: Both terms have [tex]\(\sqrt[3]{6c}\)[/tex] as a common factor.
2. Combine the coefficients: The coefficients are 5 and 7.

To combine these like terms, sum the coefficients and then multiply by the common factor [tex]\(\sqrt[3]{6c}\)[/tex].

Let's break it down:

[tex]\[ 5 \sqrt[3]{6c} + 7 \sqrt[3]{6c} \][/tex]

We sum the coefficients [tex]\(5 + 7\)[/tex]:

[tex]\[ 5 + 7 = 12 \][/tex]

Now, multiply this sum by the common factor [tex]\(\sqrt[3]{6c}\)[/tex]:

[tex]\[ 12 \sqrt[3]{6c} \][/tex]

Hence, the expression [tex]\(5 \sqrt[3]{6c} + 7 \sqrt[3]{6c}\)[/tex] is equivalent to [tex]\(12 \sqrt[3]{6c}\)[/tex].

So, the correct answer is:

C. [tex]\(12 \sqrt[3]{6c}\)[/tex]