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Sagot :
To determine which choice is equivalent to the product of [tex]\(\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{3}{9}}\)[/tex], let's break down the problem step by step.
1. Calculate [tex]\(\sqrt{\frac{3}{16}}\)[/tex]:
[tex]\[ \sqrt{\frac{3}{16}} \approx 0.433 \][/tex]
2. Calculate [tex]\(\sqrt{\frac{3}{9}}\)[/tex]:
[tex]\[ \sqrt{\frac{3}{9}} \approx 0.577 \][/tex]
3. Multiply the two square roots together:
[tex]\[ \sqrt{\frac{3}{16}} \cdot \sqrt{\frac{3}{9}} \approx 0.433 \cdot 0.577 \approx 0.25 \][/tex]
4. Convert the result to a fraction:
The decimal [tex]\(0.25\)[/tex] can be written as the fraction [tex]\(\frac{1}{4}\)[/tex].
5. Compare [tex]\(\frac{1}{4}\)[/tex] with the given choices:
[tex]\[ \begin{aligned} &A. \quad \frac{3}{12} = \frac{1}{4} \\ &B. \quad \frac{3}{4} \\ &C. \quad \frac{6}{12} = \frac{1}{2} \\ &D. \quad \frac{1}{2} \\ &E. \quad \frac{7}{12} \end{aligned} \][/tex]
The fraction [tex]\(\frac{3}{12}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex], which matches our calculated result.
Thus, the correct choice is:
[tex]\[ \boxed{\text{A}} \][/tex]
1. Calculate [tex]\(\sqrt{\frac{3}{16}}\)[/tex]:
[tex]\[ \sqrt{\frac{3}{16}} \approx 0.433 \][/tex]
2. Calculate [tex]\(\sqrt{\frac{3}{9}}\)[/tex]:
[tex]\[ \sqrt{\frac{3}{9}} \approx 0.577 \][/tex]
3. Multiply the two square roots together:
[tex]\[ \sqrt{\frac{3}{16}} \cdot \sqrt{\frac{3}{9}} \approx 0.433 \cdot 0.577 \approx 0.25 \][/tex]
4. Convert the result to a fraction:
The decimal [tex]\(0.25\)[/tex] can be written as the fraction [tex]\(\frac{1}{4}\)[/tex].
5. Compare [tex]\(\frac{1}{4}\)[/tex] with the given choices:
[tex]\[ \begin{aligned} &A. \quad \frac{3}{12} = \frac{1}{4} \\ &B. \quad \frac{3}{4} \\ &C. \quad \frac{6}{12} = \frac{1}{2} \\ &D. \quad \frac{1}{2} \\ &E. \quad \frac{7}{12} \end{aligned} \][/tex]
The fraction [tex]\(\frac{3}{12}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex], which matches our calculated result.
Thus, the correct choice is:
[tex]\[ \boxed{\text{A}} \][/tex]
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