Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Which choices are equivalent to the quotient below? Check all that apply.

[tex]\frac{\sqrt{12}}{\sqrt{6}}[/tex]

A. [tex]\frac{\sqrt{6}}{2}[/tex]

B. [tex]\frac{\sqrt{6}}{\sqrt{2}}[/tex]

C. [tex]\sqrt{2}[/tex]

D. [tex]\frac{\sqrt{4}}{\sqrt{2}}[/tex]

E. 2

F. [tex]\frac{2}{\sqrt{3}}[/tex]

Sagot :

GinnyAnswer
To determine which choices are equivalent to the quotient [tex]\(\frac{\sqrt{12}}{\sqrt{6}}\)[/tex], let us simplify the given quotient step by step.

First, consider the quotient:
[tex]\[ \frac{\sqrt{12}}{\sqrt{6}} \][/tex]

We can combine the square roots:
[tex]\[ \frac{\sqrt{12}}{\sqrt{6}} = \sqrt{\frac{12}{6}} \][/tex]

Now, simplify the fraction inside the square root:
[tex]\[ \frac{12}{6} = 2 \][/tex]

So, we have:
[tex]\[ \sqrt{\frac{12}{6}} = \sqrt{2} \][/tex]

Thus, the simplified form of the quotient is:
[tex]\[ \sqrt{2} \][/tex]

Next, we will compare this result with each of the given choices:

Choice A: [tex]\(\frac{\sqrt{6}}{2}\)[/tex]

Given as [tex]\(\frac{\sqrt{6}}{2}\)[/tex], we need to determine if this is equal to [tex]\(\sqrt{2}\)[/tex]:

Simplify [tex]\(\frac{\sqrt{6}}{2}\)[/tex]:
[tex]\[ \frac{\sqrt{6}}{2} \neq \sqrt{2} \][/tex]

So, Choice A is not correct.

Choice B: [tex]\(\frac{\sqrt{6}}{\sqrt{2}}\)[/tex]

Simplify [tex]\(\frac{\sqrt{6}}{\sqrt{2}}\)[/tex]:
[tex]\[ \frac{\sqrt{6}}{\sqrt{2}} = \sqrt{\frac{6}{2}} = \sqrt{3} \][/tex]

So, [tex]\(\sqrt{3} \neq \sqrt{2}\)[/tex]:

Choice B is not correct.

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

Given that [tex]\(\sqrt{2}\)[/tex] is already simplified, it is clear:
[tex]\[ \sqrt{2} = \sqrt{2} \][/tex]

So, Choice C is correct.

Choice D: [tex]\(\frac{\sqrt{4}}{\sqrt{2}}\)[/tex]

Simplify [tex]\(\frac{\sqrt{4}}{\sqrt{2}}\)[/tex]:
[tex]\[ \frac{\sqrt{4}}{\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2} \][/tex]

So, [tex]\(\sqrt{2} = \sqrt{2}\)[/tex]:

Choice D is correct.

Choice E: 2

Given the constant 2:
[tex]\[ 2 \neq \sqrt{2} \][/tex]

So, Choice E is not correct.

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

Simplify [tex]\(\frac{2}{\sqrt{3}}\)[/tex]:
[tex]\[ \frac{2}{\sqrt{3}} \neq \sqrt{2} \][/tex]

So, Choice F is not correct.

Based on the simplifications, the correct choices that are equivalent to [tex]\(\frac{\sqrt{12}}{\sqrt{6}}\)[/tex] are:

[tex]\[ \boxed{C} \quad \boxed{D} \][/tex]

Thus, choices C and D are equivalent to the quotient [tex]\(\frac{\sqrt{12}}{\sqrt{6}}\)[/tex].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.