Solve your doubts and expand your knowledge with IDNLearn.com's extensive Q&A database. Our experts provide timely and precise responses to help you understand and solve any issue you face.
Sagot :
To determine which choice is equivalent to the product [tex]\(\sqrt{2} \cdot \sqrt{8} \cdot \sqrt{4}\)[/tex], let's simplify the expression step-by-step.
1. Simplify the square roots:
- [tex]\(\sqrt{2}\)[/tex] remains as [tex]\(\sqrt{2}\)[/tex].
- [tex]\(\sqrt{8}\)[/tex] can be simplified. Since [tex]\(8 = 4 \times 2\)[/tex], this becomes [tex]\(\sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}\)[/tex].
- [tex]\(\sqrt{4}\)[/tex] simplifies directly to 2, because [tex]\(4 = 2^2\)[/tex] and the square root of 4 is 2.
2. Rewrite the product using these simplified forms:
[tex]\[ \sqrt{2} \cdot \sqrt{8} \cdot \sqrt{4} = \sqrt{2} \cdot (2\sqrt{2}) \cdot 2 \][/tex]
3. Combine the terms:
- First, combine [tex]\(\sqrt{2}\)[/tex] and [tex]\(2\sqrt{2}\)[/tex]:
[tex]\[ \sqrt{2} \cdot 2\sqrt{2} = 2 \cdot (\sqrt{2} \cdot \sqrt{2}) = 2 \cdot 2 = 4 \][/tex]
- Then, multiply this result by 2:
[tex]\[ 4 \cdot 2 = 8 \][/tex]
Thus, the expression [tex]\(\sqrt{2} \cdot \sqrt{8} \cdot \sqrt{4}\)[/tex] simplifies to 8.
Therefore, the correct choice is [tex]\( \text{D. } 8 \)[/tex].
1. Simplify the square roots:
- [tex]\(\sqrt{2}\)[/tex] remains as [tex]\(\sqrt{2}\)[/tex].
- [tex]\(\sqrt{8}\)[/tex] can be simplified. Since [tex]\(8 = 4 \times 2\)[/tex], this becomes [tex]\(\sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}\)[/tex].
- [tex]\(\sqrt{4}\)[/tex] simplifies directly to 2, because [tex]\(4 = 2^2\)[/tex] and the square root of 4 is 2.
2. Rewrite the product using these simplified forms:
[tex]\[ \sqrt{2} \cdot \sqrt{8} \cdot \sqrt{4} = \sqrt{2} \cdot (2\sqrt{2}) \cdot 2 \][/tex]
3. Combine the terms:
- First, combine [tex]\(\sqrt{2}\)[/tex] and [tex]\(2\sqrt{2}\)[/tex]:
[tex]\[ \sqrt{2} \cdot 2\sqrt{2} = 2 \cdot (\sqrt{2} \cdot \sqrt{2}) = 2 \cdot 2 = 4 \][/tex]
- Then, multiply this result by 2:
[tex]\[ 4 \cdot 2 = 8 \][/tex]
Thus, the expression [tex]\(\sqrt{2} \cdot \sqrt{8} \cdot \sqrt{4}\)[/tex] simplifies to 8.
Therefore, the correct choice is [tex]\( \text{D. } 8 \)[/tex].
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.