### Instruction: Calculate $\sqrt{30p} \cdot \sqrt{5p} \cdot \sqrt{6p}$ . Express your answer in simplest radical form in terms of $p$.### Response: To simplify the product of radicals, I can use the property that $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ for any positive numbers $a$ and $b$.
Applying this property to the given expression, I get $\sqrt{30p} \cdot \sqrt{5p} \cdot \sqrt{6p} = \sqrt{(30p)(5p)(6p)}$.
Next, I can simplify the radicand by multiplying the factors and looking for perfect squares.
I get $\sqrt{(30p)(5p)(6p)} = \sqrt{900p^3}$.
Now I can rewrite the radicand as a product of a perfect square and another factor.
I get $\sqrt{900p^3} = \sqrt{(30p)^2 \cdot p}$.
Using the property of radicals again, I can split the square root into two factors.
I get $\sqrt{(30p)^2 \cdot p} = \sqrt{(30p)^2} \cdot \sqrt{p}$.
Finally, I can simplify the square root of a perfect square.
I get $\sqrt{(30p)^2} \cdot \sqrt{p} = 30p \cdot \sqrt{p}$.