Square Root of 43000
2026-02-28 13:44 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-43000

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 43000, we need to group it as 00 and 430.

Step 2: Now we need to find n whose square is less than or equal to 430. We can say n as ‘20’ because 20 x 20 = 400 is lesser than 430. Now the quotient is 20 after subtracting 400 from 430, the remainder is 30.

Step 3: Now let us bring down 00 which is the new dividend. Add the old divisor with the same number, 20 + 20, we get 40 which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 40n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 40n × n ≤ 3000. Let us consider n as 7, now 407 x 7 = 2849.

Step 6: Subtract 2849 from 3000, the difference is 151, and the quotient is 207.

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 15100.

Step 8: Now we need to find the new divisor that is 414 because 414 x 3 = 1242.

Step 9: Subtracting 1242 from 15100 we get the result 25858.

Step 10: Now the quotient is 207.3.

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 √43000 ≈ 207.36.