Square Root of 1721
2026-02-28 23:17 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1721

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 1721, we need to group it as 21 and 17.

Step 2: Now we need to find n whose square is less than or equal to 17. We can say n is ‘4’ because 4 x 4 = 16, which is less than 17. Now the quotient is 4, and after subtracting 16 from 17, the remainder is 1.

Step 3: Now let us bring down 21, which is the new dividend. Add the old divisor with the same number, 4 + 4, we get 8, which will be our new divisor.

Step 4: The new divisor will be 8n. We need to find the value of n such that 8n x n is less than or equal to 121.

Step 5: Let us consider n as 1; now, 81 x 1 = 81.

Step 6: Subtract 81 from 121; the difference is 40, 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 4000.

Step 8: Now we need to find the new divisor, which is 829 because 829 x 5 = 4145.

Step 9: Subtracting 4145 from 4000, we get the result -145.

Step 10: Now the quotient is 41.47.

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

So the square root of √1721 is approximately 41.472.