To solve the product [tex]\(\sqrt{30} \cdot \sqrt{10}\)[/tex], we start with the properties of square roots. Specifically, we use the property that the product of two square roots is the square root of the product of the two numbers:
[tex]\[
\sqrt{30} \cdot \sqrt{10} = \sqrt{30 \cdot 10}
\][/tex]
Next, we calculate the product inside the square root:
[tex]\[
30 \cdot 10 = 300
\][/tex]
Thus, the expression simplifies to:
[tex]\[
\sqrt{30} \cdot \sqrt{10} = \sqrt{300}
\][/tex]
Now, we need to simplify [tex]\(\sqrt{300}\)[/tex]. Notice that 300 can be factored into:
[tex]\[
300 = 100 \cdot 3
\][/tex]
Since the square root of a product is the product of the square roots:
[tex]\[
\sqrt{300} = \sqrt{100 \cdot 3} = \sqrt{100} \cdot \sqrt{3}
\][/tex]
We know that:
[tex]\[
\sqrt{100} = 10
\][/tex]
So, substituting back, we obtain:
[tex]\[
\sqrt{300} = 10 \cdot \sqrt{3}
\][/tex]
The simplified form of the expression [tex]\(\sqrt{30} \cdot \sqrt{10}\)[/tex] is:
[tex]\[
\sqrt{30} \cdot \sqrt{10} = 10 \sqrt{3}
\][/tex]
Thus, the correct answer is:
[tex]\[
10 \sqrt{3}
\][/tex]
