Answer :

GinnyAnswer
To solve the product [tex]\(\sqrt{14} \cdot \sqrt{6}\)[/tex], we can use the property of square roots that states [tex]\(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\)[/tex].

Step-by-step solution:

1. Identify the expression to simplify:
[tex]\[ \sqrt{14} \cdot \sqrt{6} \][/tex]

2. Use the property of square roots mentioned above:
[tex]\[ \sqrt{14} \cdot \sqrt{6} = \sqrt{14 \cdot 6} \][/tex]

3. Multiply the numbers inside the square root:
[tex]\[ 14 \cdot 6 = 84 \][/tex]
Thus,
[tex]\[ \sqrt{14} \cdot \sqrt{6} = \sqrt{84} \][/tex]

4. Simplify [tex]\(\sqrt{84}\)[/tex] if possible by factoring it into a product of square roots. Notice that [tex]\(84\)[/tex] can be factored as:
[tex]\[ 84 = 4 \cdot 21 \][/tex]
Therefore,
[tex]\[ \sqrt{84} = \sqrt{4 \cdot 21} \][/tex]

5. Use the property of square roots to separate them:
[tex]\[ \sqrt{4 \cdot 21} = \sqrt{4} \cdot \sqrt{21} \][/tex]

6. Simplify [tex]\(\sqrt{4}\)[/tex] since 4 is a perfect square:
[tex]\[ \sqrt{4} = 2 \][/tex]
Therefore,
[tex]\[ \sqrt{4} \cdot \sqrt{21} = 2 \cdot \sqrt{21} \][/tex]

So, we get:
[tex]\[ \sqrt{14} \cdot \sqrt{6} = 2 \sqrt{21} \][/tex]

Hence, the correct choice is:

B. [tex]\(2 \sqrt{21}\)[/tex]

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