What is the product of the radical expression 7√28√2?

To find the product of the expression 7√28√2, we can start by breaking it down step by step.

1. **Evaluate √28**:

We can simplify √28 because 28 can be factored into prime factors:

• 28 = 4 × 7

Since 4 is a perfect square, we can take its square root:

• √28 = √(4 × 7) = √4 × √7 = 2√7

2. **Substituting back**:

Now we replace √28 in the original expression:

• 7√28√2 = 7(2√7)√2

3. **Multiply the constants**:

Now, we can multiply the constants:

• 7 × 2 = 14

So we have:

• 14√7√2

4. **Combine the radicals**:

Next, we can combine the square roots:

• √7√2 = √(7 × 2) = √14

5. **Final product**:

Putting it all together, we get:

• 7√28√2 = 14√14

Thus, the product of the radical expression 7√28√2 simplifies to:

14√14