What is the square root of 196

The square root of 196 is 14.

To find the square root of 196, you can use a calculator or apply the method of prime factorization.

Using a calculator:

1. Enter '196' on your calculator.
2. Press the square root (√) button.
3. The result should be 14, since the square root of 196 is 14.

Using prime factorization:

1. Begin by finding the prime factors of 196. Start by dividing the number by the smallest prime, which is 2.
196 ÷ 2 = 98

2. Continue dividing the quotient by 2 until you cannot divide anymore.
98 ÷ 2 = 49

3. Now, try dividing the quotient (49) by the next prime number, which is 3. However, 49 is not divisible by 3.

4. Proceed to the next prime number, which is 5.
49 ÷ 5 = 9.8

5. Since 9.8 is not a whole number, continue to the next prime number, which is 7. Again, 9.8 is not divisible by 7.

6. Next, try dividing the quotient by 11.
9.8 ÷ 11 = 0.89

7. Since 0.89 is already less than the next prime number, which is 11, we can conclude that we have found all the prime factors.

8. Now, multiply all the prime factors together to find the square root.
Square root of 196 = 2 * 2 * 7 = 14

So, the square root of 196 is 14.

To find the square root of 196, follow these steps:

Step 1: Start with any initial approximation. Let's use 10.

Step 2: Divide the number you want to find the square root of (196) by the initial approximation (10).

196 / 10 = 19.6

Step 3: Take the average of the result obtained in step 2 and the initial approximation.

(10 + 19.6)/2 = 29.8/2 = 14.9

Step 4: Repeat steps 2 and 3 until the approximation becomes accurate enough. Let's do one more iteration.

196 / 14.9 = 13.16

(14.9 + 13.16)/2 = 28.06/2 = 14.03

Step 5: Repeat step 4 until the approximation becomes accurate enough.

196 / 14.03 = 14.01

(14.03 + 14.01)/2 = 28.04/2 = 14.02

Step 6: Repeat step 4 again.

196 / 14.02 = 14.00

(14.02 + 14.00)/2 = 28.02/2 = 14.01

Since the approximation 14.01 is accurate enough, the square root of 196 is approximately 14.01.