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
multipleQuestions newQuestion Which one of the following is the rationalizing factor of the number (1)/([3]3)? newAnswer The rationalizing factor of the number (1)/([3]3) is [3]3. Explanation: A rationalizing factor of an irrational number is a factor that, when multiplied by the irrational number, results in a rational number. Let the given number be N = (1)/([3]3). We need to find an option F such that N × F is a rational number. Let's test each option: a. [3]3 Multiply N by [3]3: N × [3]3 = (1)/([3]3) × [3]3 = 1 Since 1 is a rational number, [3]3 is a rationalizing factor. b. [3]9 Multiply N by [3]9: N × 3]9 = (1)/([3]3) × [3]9 = [3/(3) = [3]3 Since [3]3 is an irrational number, [3]9 is not a rationalizing factor for N. c. sqrt(3) Multiply N by sqrt(3): N × sqrt(3) = (1)/([3]3) × sqrt(3) = 3^-1/3 × 3^1/2 = 3^(1/2) - (1/3) = 3^(3-2)/6 = 3^1/6 = [6]3 Since [6]3 is an irrational number, sqrt(3) is not a rationalizing factor for N. *d. 3 Multiply N by 3: N × 3 = (1)/([3]3) × 3 = 3 × 3^-1/3 = 3^1 - (1/3) = 3^2/3 = [3]9 Since [3]9 is an irrational number, 3 is not a rationalizing factor for N. Only option a, [3]3, results in a rational number when multiplied by (1)/([3]3).