Find solutions to your problems with the help of IDNLearn.com's expert community. Ask anything and receive thorough, reliable answers from our community of experienced professionals.
Sagot :
To determine which choice is equivalent to [tex]\(\frac{\sqrt{12}}{2 \sqrt{2}}\)[/tex], we need to simplify the expression step-by-step.
1. Simplify [tex]\(\frac{\sqrt{12}}{2 \sqrt{2}}\)[/tex]
First, recall that [tex]\(\sqrt{12}\)[/tex] can be expressed as:
[tex]\[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \][/tex]
Substitute this into the original expression:
[tex]\[ \frac{2\sqrt{3}}{2 \sqrt{2}} \][/tex]
2. Cancel out common factors in the numerator and the denominator:
[tex]\[ \frac{2\sqrt{3}}{2 \sqrt{2}} = \frac{\sqrt{3}}{\sqrt{2}} \][/tex]
3. Rationalize the denominator:
Multiply the numerator and the denominator by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ \frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{3} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{\sqrt{6}}{2} \][/tex]
The simplified expression is:
[tex]\[ \frac{\sqrt{6}}{2} \][/tex]
4. Compare with the given choices:
- Choice A: [tex]\(\frac{\sqrt{6}}{2}\)[/tex]
- Choice B: [tex]\(\sqrt{3}\)[/tex]
- Choice C: [tex]\(\frac{\sqrt{6}}{\sqrt{2}}\)[/tex]
- Choice D: [tex]\(\frac{\sqrt{6}}{4}\)[/tex]
Based on our simplification, the expression [tex]\(\frac{\sqrt{6}}{2}\)[/tex] matches Choice A.
Therefore, the equivalent expression to [tex]\(\frac{\sqrt{12}}{2 \sqrt{2}}\)[/tex] is given by:
[tex]\[ \boxed{\frac{\sqrt{6}}{2}} \][/tex]
The correct choice is A.
1. Simplify [tex]\(\frac{\sqrt{12}}{2 \sqrt{2}}\)[/tex]
First, recall that [tex]\(\sqrt{12}\)[/tex] can be expressed as:
[tex]\[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \][/tex]
Substitute this into the original expression:
[tex]\[ \frac{2\sqrt{3}}{2 \sqrt{2}} \][/tex]
2. Cancel out common factors in the numerator and the denominator:
[tex]\[ \frac{2\sqrt{3}}{2 \sqrt{2}} = \frac{\sqrt{3}}{\sqrt{2}} \][/tex]
3. Rationalize the denominator:
Multiply the numerator and the denominator by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ \frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{3} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{\sqrt{6}}{2} \][/tex]
The simplified expression is:
[tex]\[ \frac{\sqrt{6}}{2} \][/tex]
4. Compare with the given choices:
- Choice A: [tex]\(\frac{\sqrt{6}}{2}\)[/tex]
- Choice B: [tex]\(\sqrt{3}\)[/tex]
- Choice C: [tex]\(\frac{\sqrt{6}}{\sqrt{2}}\)[/tex]
- Choice D: [tex]\(\frac{\sqrt{6}}{4}\)[/tex]
Based on our simplification, the expression [tex]\(\frac{\sqrt{6}}{2}\)[/tex] matches Choice A.
Therefore, the equivalent expression to [tex]\(\frac{\sqrt{12}}{2 \sqrt{2}}\)[/tex] is given by:
[tex]\[ \boxed{\frac{\sqrt{6}}{2}} \][/tex]
The correct choice is A.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.