**Simplifying (10 √3)(6 √2)**

To simplify the expression (10 √3)(6 √2), we need to use the distributive property of multiplication over addition.

**Step 1: Multiply the coefficients**

The first step is to multiply the coefficients (the numbers outside the square roots) together. In this case, we have:

10 x 6 = 60

**Step 2: Multiply the radicands**

Next, we need to multiply the radicands (the numbers inside the square roots) together. In this case, we have:

√3 x √2 = √(3 x 2) = √6

**Step 3: Combine the results**

Finally, we combine the results from steps 1 and 2 to get our final answer:

(10 √3)(6 √2) = 60√6

Therefore, the simplified expression is 60√6.

**Explanation**

The expression (10 √3)(6 √2) can be simplified using the distributive property of multiplication. This property states that when we multiply a term by a sum or difference, we can distribute the term to each individual term and then add or subtract the results. In this case, we have two terms that we need to distribute:

(10 √3)(6 √2) = 10 x 6 √3 x √2

We can simplify this expression by multiplying the coefficients together and then multiplying the radicands together:

10 x 6 = 60

√3 x √2 = √6

Finally, we combine the results to get our final answer:

(10 √3)(6 √2) = 60√6

Therefore, the simplified expression is 60√6.

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