### Instruction: Calculate $\sqrt{75x} \cdot \sqrt{2x} \cdot \sqrt{14x}$ . Express your answer in simplest radical form in terms of $x$.### Response: To simplify this product of square roots, I can use the property that $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ for any positive numbers $a$ and $b$.
So I can rewrite the product as $\sqrt{75x \cdot 2x \cdot 14x}$.
Now I can simplify the expression inside the square root by multiplying the numbers and the powers of $x$.
I get $\sqrt{2100x^3}$.
To simplify further, I can look for perfect square factors in the number 2100.
I notice that 100 is a perfect square, and 2100 = 100 \cdot 21.
So I can write $\sqrt{2100x^3} = \sqrt{100x^2} \cdot \sqrt{21x}$.
Then I can take the square root of 100 and the square root of $x^2$, since they are both positive.
I get $\sqrt{100x^2} \cdot \sqrt{21x} = 10x \cdot \sqrt{21x}$.
This is the simplest radical form of the expression, since 21 has no perfect square factors.