For example, the square root of 25 is 5 because 5 x 5 = 25. In this article, we will discuss how to find square roots using different methods such as long division and estimation by prime factorization.

To calculate a square root using long division:
1. Write down the number for which you want to find the square root. For example, let’s say we want to find the square root of 81.
2. Divide the first digit (in this case, 8) by 2 and write it above the line as a fraction with 1 in the denominator: 4/1.
3. Multiply the result from step 2 by itself to get an estimate for the square root. In our example, 4 x 4 = 16. Since we’re looking for the square root of 81, this is too big. We need to adjust our guess downward.
4. Divide the original number (in this case, 81) by the result from step 3: 81/16 = 5. This gives us a new estimate for the square root: approximately 5.
5. Repeat steps 2-4 until you get an answer that is accurate enough for your needs. In our example, we could continue dividing by 2 and multiplying by itself to refine our guess: 4/1 = 2; 2 x 2 = 4; 81/16 = 5; 5 x 5 = 25 (which is too big); 50/100 = 0.5; 0.5 x 0.5 = 0.25 (our final answer).

To calculate a square root using estimation by prime factorization:
1. Write down the number for which you want to find the square root. For example, let’s say we want to find the square root of 64.
2. Find all the factors that are perfect squares (i.e., numbers that can be multiplied together to get a perfect square). In our example, these would be 1 x 1 = 1 and 8 x 8 = 64.
3. Divide each factor by its corresponding prime factor: in this case, we divide both 1 and 8 by their respective primes (which are 2): 1/2 = 0.5; 8/2^3 = 2. This gives us an estimate for the square root of 64: approximately 4.
4. Check your answer using a calculator or other method to see if it’s accurate enough for your needs. If not, adjust your guess accordingly and repeat steps 1-4 until you get an answer that is close enough to the actual value.