Square Root of 1440
2026-02-28 01:08 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1440

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 1440, we need to group it as 40 and 14.

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

Step 3: Now let us bring down 40, which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 540. Let us consider n as 9, now 69 × 9 = 621, which is greater than 540. Trying n as 8, we get 68 × 8 = 544, which is slightly greater, so n is 7 here.

Step 6: Subtract 544 from 540, the difference is -4, and the quotient is 37.

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 that is 759 because 759 × 5 = 3795.

Step 9: Subtracting 3795 from 4000, we get the result 205.

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 are no decimal values, continue till the remainder is zero.

So the square root of √1440 is approximately 37.95.