How do you simplify the square root of 28 times the square root of 14?

To simplify the expression √28 × √14, we can follow these steps:

Step 1: Use the property of square roots:
The product of two square roots can be combined into a single square root:
√28 × √14 = √(28 × 14)

Step 2: Multiply the numbers under the square root:
28 × 14 = 392
So, √(28 × 14) = √392.

Step 3: Simplify the square root of 392 by finding its prime factorization:
392 = 2 × 2 × 2 × 7 × 7
Group the factors into pairs: (2 × 2), (7 × 7), and a single 2 remains unpaired.

Step 4: Take the square root of the paired factors:
The square root of (2 × 2) is 2, and the square root of (7 × 7) is 7. The unpaired 2 stays under the square root.
So, √392 = 2 × 7 × √2 = 14√2.

Final Answer:
The simplified form of √28 × √14 is 14√2.