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
Let's solve this step by step. Step 1: Factor 26010 into its prime factors. 26010 = 2 × 3 × 5 × 7 × 13 Step 2: For a number to be a perfect square, all prime factors must have even exponents. Currently, the exponents of the prime factors are: 2: 1 (odd) 3: 1 (odd) 5: 1 (odd) 7: 1 (odd) 13: 1 (odd) Step 3: To make each exponent even, we need to multiply by each prime factor that has an odd exponent. Therefore, we need to multiply by: p = 2 × 3 × 5 × 7 × 13 Step 4: Calculate p. p = 2 × 3 × 5 × 7 × 13 = 2730 Step 5: The smallest possible p such that 26010p is a square number is 2730. Got more? Send 'em 📸