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Which choice is equivalent to the product below?

[tex]\(\sqrt{2} \cdot \sqrt{10} \cdot \sqrt{5}\)[/tex]

A. [tex]\(5 \sqrt{2}\)[/tex]
B. 10
C. [tex]\(2 \sqrt{50}\)[/tex]
D. [tex]\(4 \sqrt{25}\)[/tex]

Sagot :

GinnyAnswer
To determine which choice is equivalent to the product [tex]\(\sqrt{2} \cdot \sqrt{10} \cdot \sqrt{5}\)[/tex], let's go through a step-by-step simplification process.

1. Write the product of the square roots as a single square root:
[tex]\[ \sqrt{2} \cdot \sqrt{10} \cdot \sqrt{5} = \sqrt{2 \cdot 10 \cdot 5} \][/tex]

2. Simplify the expression inside the square root:
[tex]\[ 2 \cdot 10 \cdot 5 = 100 \][/tex]

3. Take the square root of the resulting product:
[tex]\[ \sqrt{100} = 10 \][/tex]

Thus, the product [tex]\(\sqrt{2} \cdot \sqrt{10} \cdot \sqrt{5}\)[/tex] simplifies to [tex]\(10\)[/tex].

So the correct choice is:

B. 10
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