Square Root of 19.6
2026-02-28 08:17 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-19.6

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 19.6, we can consider it as 196/10 to simplify.

Step 2: Now we need to find n whose square is less than or equal to 19. We can say n is 4 because 4 × 4 = 16, which is less than 19. Now the quotient is 4, and after subtracting 16 from 19, the remainder is 3.

Step 3: Now, let us bring down 60, making it 360. Add the old divisor with the same number: 4 + 4 = 8, which will be our new divisor.

Step 4: The new divisor will be 8n. We need to find the value of n where 8n × n ≤ 360. Let us consider n as 4, now 84 × 4 = 336.

Step 5: Subtract 336 from 360, and the difference is 24. The quotient becomes 4.4.

Step 6: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2400.

Step 7: Now we need to find the new divisor, which is 88 because 884 × 4 = 3536 is more than 2400, so the previous divisor works.

Step 8: Subtract 1760 from 2400 to get the remainder 640. Continue this process until you achieve the desired precision.

The square root of 19.6 is approximately 4.427.