Square Root of 2989
2026-02-28 10:50 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2989

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 2989, we need to group it as 89 and 29.

Step 2: Now we need to find n whose square is less than or equal to 29. We can say n as ‘5’ because 5 x 5 = 25, which is less than 29. Now the quotient is 5, and after subtracting 25 from 29, the remainder is 4.

Step 3: Now let us bring down 89, which is the new dividend. Add the old divisor with the same number 5 + 5, we get 10, which will be our new divisor.

Step 4: The new divisor will be 10n. We need to find the value of n such that 10n x n is less than or equal to 489.

Step 5: The next step is finding 10n x n ≤ 489. Let us consider n as 4, now 104 x 4 = 416.

Step 6: Subtract 416 from 489; the difference is 73, and the quotient is 54.

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 7300.

Step 8: Now we need to find the new divisor that is 109 because 1099 x 9 = 9891, which is less than 7300.

Step 9: Subtracting 9891 from 7300; we get the result 1591.

Step 10: Now the quotient is 54.6

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero. So the square root of √2989 is approximately 54.68.