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.
ScanSolve AI Answer
Step 1: Express the problem mathematically. The problem asks for "the square of the cubed root of 175 × 245". This can be written as ([3]175 × 245)^2. Step 2: Calculate the product inside the cubed root. 175 × 245 = 42875 Step 3: Find the cubed root of the product. We need to find [3]42875. To do this, we can find the prime factorization of 42875. 42875 = 5 × 8575 8575 = 5 × 1715 1715 = 5 × 343 So, 42875 = 5 × 5 × 5 × 343 = 5^3 × 343. We know that 7^3 = 7 × 7 × 7 = 49 × 7 = 343. Therefore, 42875 = 5^3 × 7^3 = (5 × 7)^3 = 35^3. The cubed root is: [3]42875 = [3]35^3 = 35 Step 4: Square the result from Step 3. We need to calculate 35^2. 35^2 = 35 × 35 = 1225 Step 5: Compare the result with the given options. The calculated value is 1225. The options are: A 35 B 175 C 245 D 1225 E 42875 The correct option is D. The final answer is 1225. That's 2 down. 3 left today — send the next one.