Square Root of 196


Finding the square root of a number involves determining the value that, when multiplied by itself, gives the original number. In this case, we are looking for the square root of 196.


To find the square root of 196, we can use a few different methods. Let's explore two common methods: prime factorization and long division.


1. Begin by expressing the number 196 as a product of its prime factors.
- The prime factorization of 196 is 2^2 * 7^2.
2. Take one factor from each pair of prime factors and multiply them together.
- In this case, we take one 2 and one 7, resulting in 2 * 7 = 14.
3. The product obtained in step 2 is the square root of 196.
- Therefore, the square root of 196 is 14.


1. Start by writing down the number 196.
2. Divide the number into pairs of digits starting from the right.
- We have 19 and 6 as the pairs.
3. Find the largest number whose square is less than or equal to 19.
- The largest number whose square is less than or equal to 19 is 4.
4. Write the divisor (4) above the division line and the quotient (also 4) below.
5. Multiply the divisor (4) by the quotient (4) and write the product (16) below the 19.
6. Subtract the product (16) from the 19 and bring down the next pair of digits (6).
- We get 19 - 16 = 3, bring down 6.
7. Double the quotient (4) and write it on the left of the 6.
- We get 46.
8. Find a number to fill in the blank in the quotient, so that when it is multiplied by the new divisor, the product is less than or equal to the dividend.
- In this case, the new divisor is 8, and the largest number that can be multiplied by 8 to get a product less than or equal to 36 is 4.
9. Write the new divisor (48) above the division line and the new quotient (also 4) below.
10. Multiply the new divisor (48) by the new quotient (4) and write the product (32) below the 36.
11. Subtract the product (32) from the 36, and there are no more digits to bring down.
- We get 36 - 32 = 4.
12. The final quotient is the square root of 196.
- Therefore, the square root of 196 is 14.


Using either the prime factorization method or the long division method, we find that the square root of 196 is 14.