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
Here are the solutions to the problems. Problem 3: Which of the following are squares of odd numbers? To determine if a number is the square of an odd number, we find its square root and check if the root is an odd number. Step 1: Check (i) 484 sqrt(484) = 22 Since 22 is an even number, 484 is the square of an even number. Step 2: Check (ii) 961 sqrt(961) = 31 Since 31 is an odd number, 961 is the square of an odd number. Step 3: Check (iii) 7396 sqrt(7396) = 86 Since 86 is an even number, 7396 is the square of an even number. Step 4: Check (iv) 8649 (assuming the partially visible number is 8649) sqrt(8649) = 93 Since 93 is an odd number, 8649 is the square of an odd number. Step 5: Check (v) 4225 sqrt(4225) = 65 Since 65 is an odd number, 4225 is the square of an odd number. The numbers that are squares of odd numbers are (ii) 961, (iv) 8649, and (v) 4225. (ii) 961, (iv) 8649, (v) 4225 --- Problem 4: Without adding, find the sum: We use the property that the sum of the first n odd numbers is n^2. a) For (i) 1+3+5+7+9+11+13 Step 1: Count the number of terms. There are 7 odd numbers in the sequence. So, n=7. Step 2: Calculate the sum. The sum is n^2 = 7^2 = 49. 49 b) For (ii) (1+3+5+7+9+11+13+1...) This expression is incomplete and cannot be solved accurately. c) For (iii) 1+3+5+7+9+11+13+15+17+19+21+23 Step 1: Count the number of terms. There are 12 odd numbers in the sequence. So, n=12. Step 2: Calculate the sum. The sum is n^2 = 12^2 = 144. 144 What's next? Send 'em! 📸