Square Root of 1344
2026-02-28 21:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1344

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 1344, we need to group it as 44 and 13.

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

Step 3: Now let us bring down 44, 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, and we need to find the value of n.

Step 5: The next step is finding such n that 6n × n ≤ 444. Let us consider n as 7, now 67 × 7 = 469.

Step 6: Since 469 is greater than 444, we try n as 6. Now 66 × 6 = 396.

Step 7: Subtract 396 from 444, the difference is 48, and the quotient is 36.

Step 8: 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 4800.

Step 9: We find the new divisor as 732 because 732 × 6 = 4392.

Step 10: Subtracting 4392 from 4800, we get the result 408.

Step 11: Now the quotient is 36.6. Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.

So the square root of √1344 is approximately 36.66.