Square Root of 2669
2026-02-28 08:32 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2669

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 2669, we need to group it as 69 and 26.

Step 2: Now we need to find n whose square is less than or equal to 26. We can say n is ‘5’ because 5 x 5 = 25 is less than 26. Now the quotient is 5, and after subtracting 25 from 26, the remainder is 1.

Step 3: Bring down the next pair, which is 69, making the new dividend 169. Add the old divisor with the same number 5 + 5 to get 10, which will be our new divisor.

Step 4: Now find n such that 10n x n ≤ 169. We try n = 1, giving us 101 x 1 = 101.

Step 5: Subtract 101 from 169, the difference is 68, and the quotient is 51.

Step 6: 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 6800.

Step 7: Now find the new divisor. We try n = 6 as 1036 x 6 = 6216.

Step 8: Subtracting 6216 from 6800, we get 584.

Step 9: Now the quotient is 51.6.

Step 10: Continue doing these steps until we get a sufficient number of decimal places.

So the square root of √2669 is approximately 51.67.