This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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: Step 1: Calculate the square roots and the exponent. Step 2: Perform the subtraction in the numerator and the addition in the denominator. Step 3: Perform the division. The value is .
: Step 1: Calculate the square root. Step 2: Perform the subtraction. The value is .
: Step 1: Calculate the square roots inside the parentheses. Step 2: Perform the multiplication and addition inside the parentheses. Step 3: Perform the addition. The value is .
: Step 1: Calculate the exponent and the square root. Step 2: Perform the subtraction in the numerator. Step 3: Perform the division. The value is .
: Step 1: Calculate the exponent and the square root. Step 2: Perform the subtraction in the numerator. Step 3: Perform the division. The value is .
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Problem 1: sqrt(225) - sqrt(100)sqrt(16) + 1^2 Step 1: Calculate the square roots and the exponent.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.