To simplify the expression \(\sqrt{3x^4}\cdot\sqrt{5x^2}\cdot\sqrt{10}\), we first use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}\). Thus, we can combine the square roots under a single square root:
\[ \sqrt{3x^4} \cdot \sqrt{5x^2} \cdot \sqrt{10} = \sqrt{3x^4 \cdot 5x^2 \cdot 10} \]
Now we calculate the product inside the square root:
\[ 3 \cdot 5 \cdot 10 = 150 \] \[ x^4 \cdot x^2 = x^{4+2} = x^6 \]
Combining these results gives us:
\[ \sqrt{3x^4 \cdot 5x^2 \cdot 10} = \sqrt{150x^6} \]
Next, we can separate the expression inside the square root into perfect squares and the remaining factors:
\[ \sqrt{150x^6} = \sqrt{150} \cdot \sqrt{x^6} \]
The term \(\sqrt{x^6}\) can be simplified further since \(x^6\) is a perfect square:
\[ \sqrt{x^6} = x^{6/2} = x^3 \]
Now, we will simplify \(\sqrt{150}\). We start by finding the prime factorization of 150:
\[ 150 = 2 \cdot 3 \cdot 5^2 \]
The perfect square in this case is \(5^2\). Thus, we can simplify \(\sqrt{150}\):
\[ \sqrt{150} = \sqrt{2 \cdot 3 \cdot 5^2} = \sqrt{5^2} \cdot \sqrt{2 \cdot 3} = 5 \cdot \sqrt{6} \]
Putting this all together, we have:
\[ \sqrt{150} \cdot x^3 = 5 \sqrt{6} \cdot x^3 \]
Thus, the final simplified form of our original expression is:
\[ \boxed{5x^3\sqrt{6}} \]
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