Square Root of 1394
2026-02-28 01:26 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1394

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 1394, we need to group it as 94 and 13.

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

Step 3: Now let us bring down 94, 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 current quotient with the number we add in the next step. Now we look for a digit n such that 6n x n is less than or equal to 494.

Step 5: The next step is finding 6n x n ≤ 494. Let us consider n as 8, now 68 x 8 = 544, which is too high, so we try n as 7, then 67 x 7 = 469.

Step 6: Subtracting 469 from 494, the difference is 25, 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 2500.

Step 8: Now we need to find the new divisor that is 746 because 746 x 3 = 2238.

Step 9: Subtracting 2238 from 2500, we get the result 262.

Step 10: Now the quotient is 37.3

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 √1394 ≈ 37.313