Square Root of 1441
2026-02-28 08:07 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1441

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square numbers 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 1441, we need to group it as 41 and 14.

Step 2: Now we need to find n whose square is less than or equal to 14. We can say n is ‘3’ because 3 × 3 = 9, which is less than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 41, making the new dividend 541. Add the old divisor (3) with the same number (3) to get 6, which will be our new divisor.

Step 4: The new divisor will be 6n. We need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 541. Let us consider n as 8. Now 68 × 8 = 544.

Step 6: Subtract 541 from 544 to get the difference of -3, and the quotient is 38.

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 300.

Step 8: Now we need to find a new divisor: 759 because 759 × 9 = 6831.

Step 9: Subtracting 6831 from 9000, we get the result 2169.

Step 10: Now the quotient is 37.9.

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

So the square root of √1441 is approximately 37.95.