Find the square root of 196: 196−−−√ (1 point)
14
To find the square root of 196, you can either calculate it manually or use a calculator.
If you choose to calculate it manually:
1. Start by finding the prime factorization of 196:
196 = 2 * 2 * 7 * 7
2. Pair up the prime factors and take one of each as a square root:
√(2 * 2 * 7 * 7) = 2 * 7 = 14
Therefore, the square root of 196 is 14.
To find the square root of 196, you can use a calculator or do it manually.
Using a calculator:
1. Type in "196" into the calculator.
2. Press the square root (√) button.
3. The calculator should give you the result, which is 14.
Manually:
1. Start with an estimated guess. In this case, let's start with 10.
2. Square the number you guessed: 10^2 = 100.
3. If the square is less than 196, increase your guess and repeat step 2.
- Guess: 11. Square: 11^2 = 121 (less than 196).
- Guess: 12. Square: 12^2 = 144 (less than 196).
- Guess: 13. Square: 13^2 = 169 (less than 196).
- Guess: 14. Square: 14^2 = 196 (equal to 196).
4. We have found that the square root of 196 is 14.
Therefore, the square root of 196 is 14.