Square Root of 1428
2026-02-28 11:16 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1428

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 1428, we need to group it as 28 and 14.

Step 2: Now we need to find n whose square is 14. We can say n as '3' because 3 x 3 is 9, which is lesser than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 28, which is the new dividend. Add the old divisor with the same number 3 + 3 to 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 x n ≤ 528. Let us consider n as 8; now 68 x 8 = 544, which is too large, so try n as 7; 67 x 7 = 469.

Step 6: Subtract 469 from 528; the difference is 59, 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 5900.

Step 8: Now we need to find the new divisor, which is 759, because 759 x 7 = 5323.

Step 9: Subtracting 5323 from 5900, we get the result 577.

Step 10: Now the quotient is 37.7.

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 √1428 ≈ 37.79.