To estimate the square root of each given number, we can use a method that involves identifying potential square root values by examining the digits. Here is a detailed approach:
### a. For 2916:
1. Separate the last two digits from the rest: 29 and 16.
2. The square root of a number ending in 6 could end in either 4 or 6.
3. Approximate the square root for 29 (the remaining part):
- The nearest perfect squares to 29 are 25 (5^2) and 36 (6^2).
- The higher value is 6.
4. Combining these insights, the options are 54 or 56.
5. Since 2925 is closer to 2916, we select 54.
### b. For 3844:
1. Separate the last two digits from the rest: 38 and 44.
2. The square root of a number ending in 4 could end in either 2 or 8.
3. Approximate the square root for 38:
- Nearest squares are 36 (6^2) and 49 (7^2).
- The higher value is between 6 and 7, leaning more towards 6.
4. Combining these insights, the options are 62 or 68.
5. Given 3844's closeness to a perfect square around this range, we pick 62.
### c. For 9025:
1. Separate the last two digits from the rest: 90 and 25.
2. The square root of a number ending in 25 is 5.
3. Approximate the square root for 90:
- Nearest squares are 81 (9^2) and 100 (10^2).
- The higher value is 9.
4. Therefore, the square root ends in 95.
### d. For 144:
1. Separate the last two digits: 1 and 44.
2. The square root of a number ending in 44 is less straightforward, so we consider known squares.
3. Observing that 144 is a commonly known perfect square:
4. The square root is 12.
### e. For 676:
1. Separate the last two digits from the rest: 6 and 76.
2. The square root of a number ending in 76 could end in either 4 or 6.
3. Approximate the square root for 6:
- Seeing 676 is close to the square of 25:
4. We intelligently deduce the square root to be 26.
### f. For 4225:
1. Separate the last two digits from the rest: 42 and 25.
2. The square root of a number ending in 25 is 5.
3. Approximate the square root for 42:
- Nearest squares are 36 (6^2) and 49 (7^2).
- The higher value is 6.
4. Therefore, the square root is 65.
Thus, the estimated square roots for the numbers are:
- 2916 -> 54
- 3844 -> 62
- 9025 -> 95
- 144 -> 12
- 676 -> 26
- 4225 -> 65
