Evaluate the following: The square root of (10 + √25)(12 - √49) is:

Step-by-Step Solution

To evaluate the square root of the expression, follow these steps to simplify the terms inside the root first:

1. Simplify individual terms:

   • The expression is: sqrt((10 + sqrt(25)) * (12 - sqrt(49)))

   • First, calculate the inner square roots:

     • sqrt(25) = 5

     • sqrt(49) = 7

   • Now, substitute these values back into the expression:

     • sqrt((10 + 5) * (12 - 7))

2. Perform subtraction and addition:

   • (10 + 5) = 15

   • (12 - 7) = 5

   • The expression becomes: sqrt(15 * 5)

3. Evaluate the square root:

   • Multiply the numbers: 15 * 5 = 75

   • The expression is: sqrt(75)

   • Prime factorize 75 to simplify the radical: 75 = 3 * 5 * 5

   • sqrt(3 * 5 * 5) = 5 * sqrt(3)

Final Answer

The correct value is 5√3, which corresponds to Option C.