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
To make a number a perfect square, all the exponents in its prime factorization must be even. Step 1: Write down the prime factorization of 252. The problem states that 252 = 2^2 × 3^2 × 7. Step 2: Examine the exponents of the prime factors. The prime factor 2 has an exponent of 2 (even). The prime factor 3 has an exponent of 2 (even). The prime factor 7 has an exponent of 1 (odd). Step 3: Determine what factor is needed to make all exponents even. To make the exponent of 7 even, we need to multiply by another 7. This will change 7^1 to 7^1 × 7^1 = 7^2. So, the number to be multiplied is 7. Step 4: Verify the new product. 252 × 7 = (2^2 × 3^2 × 7) × 7 = 2^2 × 3^2 × 7^2. All exponents (2, 2, 2) are now even, so the product is a perfect square. The least number that should be multiplied by 252 to make the product a perfect square is 7. The correct option is D. D. 7 Send me the next one 📸