**Sum of Odd Numbers:**

To express a given number as the sum of odd numbers, we need to understand the concept of odd numbers and how they can be added together to yield the given number. Let's explore this concept for the given numbers:

(i) 7^2:

To find the sum of odd numbers that equals 7^2, we can start by understanding the properties of odd numbers. Odd numbers are integers that are not divisible by 2. Therefore, they can be expressed in the form of 2n+1, where n is an integer.

For 7^2, we need to find a combination of odd numbers that sum up to 49. One possible way to do this is by adding consecutive odd numbers. Let's break it down:

- 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49

Here, we have added seven consecutive odd numbers to get the desired sum of 49, which is equal to 7^2. Therefore, the sum of odd numbers that equals 7^2 is 1 + 3 + 5 + 7 + 9 + 11 + 13.

(ii) 9^2:

Similar to the previous case, we can express 9^2 as the sum of odd numbers. Let's break it down:

- 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81

Here, we have added nine consecutive odd numbers to get the desired sum of 81, which is equal to 9^2. Therefore, the sum of odd numbers that equals 9^2 is 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17.

**Summary:**

- 7^2 can be expressed as the sum of odd numbers: 1 + 3 + 5 + 7 + 9 + 11 + 13.
- 9^2 can be expressed as the sum of odd numbers: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17.

By adding consecutive odd numbers, we can find the sum that equals the given numbers. This concept is useful in various mathematical calculations and can be extended to other numbers as well.