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Select the correct answer.

What is this expression in simplified form?
[tex]\[ \sqrt{32} \cdot \sqrt{24} \][/tex]

A. [tex]\(64 \sqrt{12}\)[/tex]

B. [tex]\(16 \sqrt{3}\)[/tex]

C. [tex]\(\sqrt{768}\)[/tex]

D. [tex]\(32 \sqrt{3}\)[/tex]


Sagot :

To simplify the expression [tex]\(\sqrt{32} \cdot \sqrt{24}\)[/tex], we can use the property of square roots which states that [tex]\(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\)[/tex].

So, we have:
[tex]\[ \sqrt{32} \cdot \sqrt{24} = \sqrt{32 \cdot 24} \][/tex]

Next, we need to calculate the product inside the square root:
[tex]\[ 32 \cdot 24 = 768 \][/tex]

This simplifies our expression to:
[tex]\[ \sqrt{768} \][/tex]

There is no need to simplify this further because it already appears in one of the given options.

Upon comparing with the options provided, we see that option C matches our result.

Thus, the correct answer is:
C. [tex]\(\sqrt{768}\)[/tex]