To simplify the expression 5√6 • 2√3, we can use the properties of multiplication with square roots.
First, we multiply the coefficients (numbers outside the square roots), which are 5 and 2, giving us 10.
Next, we multiply the numbers inside the square roots, which are √6 and √3. When multiplying square roots, we can combine them under a single radical sign. Therefore, we have √6 • √3 = √(6 • 3) = √18.
Now, let's simplify √18. We can break it down further by finding the largest perfect square that divides 18, which is 9. We can rewrite √18 as √(9 • 2). Using the property of square roots, it becomes √9 • √2 = 3 • √2.
Finally, multiplying the coefficient (10) by the simplified square root (3√2), we get 10 • 3 • √2 = 30√2.
Therefore, the expression 5√6 • 2√3 is equal to 30√2.
So, the correct option is: O 30√2.