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Choose the expression that shows the correct product for [tex]\(\sqrt{3} \cdot \sqrt{12}\)[/tex].

A. [tex]\(\sqrt{15}\)[/tex]
B. [tex]\(\sqrt{36}\)[/tex]
C. [tex]\(\sqrt[4]{15}\)[/tex]
D. [tex]\(\sqrt[4]{36}\)[/tex]

Sagot :

GinnyAnswer
Let's find the correct product expression for [tex]\(\sqrt{3} \cdot \sqrt{12}\)[/tex].

First, recall the property of square roots that states:
[tex]\[ \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \][/tex]

Using this property, we can combine the square roots:
[tex]\[ \sqrt{3} \cdot \sqrt{12} = \sqrt{3 \cdot 12} \][/tex]

Next, we need to simplify the expression inside the square root:
[tex]\[ 3 \cdot 12 = 36 \][/tex]

So the product [tex]\(\sqrt{3} \cdot \sqrt{12}\)[/tex] simplifies to:
[tex]\[ \sqrt{36} \][/tex]

Hence, the correct expression that shows the correct product for [tex]\(\sqrt{3} \cdot \sqrt{12}\)[/tex] is:
[tex]\[ \sqrt{36} \][/tex]

Therefore, the correct answer is [tex]\(\boxed{\sqrt{36}}\)[/tex].
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