Final answer:
The product of the given square roots is simplified and multiplied to give a final answer of 720000.
Step-by-step explanation:
The product of the given square roots can be found by multiplying the terms under the square root first and then taking the square root of the result. The given expression is StartRoot 30 EndRoot times StartRoot 10 EndRoot 2 StartRoot 10 EndRoot 3 StartRoot 10 EndRoot 4 StartRoot 10 EndRoot 10 StartRoot 3 EndRoot, which simplifies to:
√30 * √10 * 2√10 * 3√10 * 4√10 * √3 = √(30 * 10) * 2√(10 * 10) * 3√(10 * 10) * 4√(10 * 10) * √3
By simplifying the square roots, we get:
√300 * 2(√100) * 3(√100) * 4(√100) * √3
Now, simplifying further, we get:
√300 * 2 * 10 * 3 * 10 * 4 * 10 * √3
Which gives:
10√3 * 20 * 30 * 40 * √3
Combining the square roots and multiplying the constants:
10 * √3 * √3 * 20 * 30 * 40
This simplifies to:
10 * 3 * 20 * 30 * 40
Finally, multiplying the constants gives us:
10 * 3 * 20 * 30 * 40 = 720000
Therefore, the product of the given square roots is 720000.