Square Root of 1345
2026-02-21 20:43 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1345

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 1345, we need to group it as 45 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 is less than 13. Now the quotient is 3 after subtracting 13 - 9, the remainder is 4.

Step 3: Now let us bring down 45, which is the new dividend. Add the old divisor with the same number 3 + 3, we 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 ≤ 445. Let's consider n as 7, now 67 x 7 = 469.

Step 6: Subtract 445 from 469; since 469 is greater than 445, n should be 6. So, 66 x 6 = 396.

Step 7: Subtract 396 from 445; the difference is 49, 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 4900.

Step 9: Now we need to find the new divisor. It is 732 because 732 x 6 = 4392.

Step 10: Subtracting 4392 from 4900 we get 508.

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

So the square root of √1345 is approximately 36.656.