Square Root of 1489
2026-02-28 09:10 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1489

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 1489, we need to group it as 14 and 89.

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 x 3 = 9, which is less than 14. Now the quotient is 3, after subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 89, which is the new dividend. Add the old divisor with the same number, 3 + 3 = 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 ≤ 589. Let us consider n as 9, now 69 x 9 = 621.

Step 6: Subtract 589 from 621, the difference is -32, which means n should be 8.

Step 7: The new divisor is 68. The result is 68 x 8 = 544.

Step 8: Subtracting 544 from 589 gives the remainder 45. The quotient is 38.

Step 9: 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 4500.

Step 10: Now we need to find the new divisor that is 386 because 386 x 1 = 386.

Step 11: Subtracting 386 from 4500 gives the result 4114. Step 12: Continue doing these steps until we achieve the desired precision.

The square root of √1489 is approximately 38.588.