Square Root of 1696
2026-02-28 17:19 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1696

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 1696, we need to group it as 96 and 16.

Step 2: Now we need to find n whose square is less than or equal to 16. We can say n as ‘4’ because 4 x 4 = 16. Now the quotient is 4 after subtracting 16 from 16, the remainder is 0.

Step 3: Now let us bring down 96, which is the new dividend. Add the old divisor with the same number 4 + 4 to get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and the quotient. Now we get 8n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 96. Let us consider n as 1, now 8 x 1 x 1 = 8.

Step 6: Subtract 8 from 96; the difference is 88, and the quotient is 41.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 8800.

Step 8: Now we need to find the new divisor. Let us consider n as 9 because 819 x 9 = 7371.

Step 9: Subtracting 7371 from 8800, we get the result 1429.

Step 10: Now the quotient is 41.1

Step 11: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.

So the square root of √1696 is approximately 41.18.