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]
