Square Root of 1322
2026-02-28 11:45 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1322

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 1322, we need to group it as 22 and 13.

Step 2: Now we need to find n whose square is less than or equal to 13. We can say n as ‘3’ because 3 x 3 = 9, which is less than 13. Now the quotient is 3, and after subtracting, 13 - 9, the remainder is 4.

Step 3: Bring down the next pair of numbers, which is 22, making the new dividend 422. Add the old divisor, 3, with itself, giving us 6, which will be part of our new divisor, 6n.

Step 4: We need to find n such that 6n x n ≤ 422. Let us consider n as 6, then 66 x 6 = 396, which is less than 422.

Step 5: Subtract 396 from 422, giving a remainder of 26, and the quotient is 36.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point and bring down two zeros. The new dividend is 2600.

Step 7: Find a new digit for the divisor to be used with the new dividend. This digit is 4 because 724 x 4 = 2896, which exceeds 2600. We try 3, giving us 723 x 3 = 2169.

Step 8: Subtract 2169 from 2600, yielding 431. The quotient now is 36.3.

Step 9: Continue these steps by bringing down more pairs of zeros, refining the remainder, and extending the quotient.