Square Root of 3200
2026-02-28 15:49 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3200

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 3200, we need to group it as 00 and 32.

Step 2: Now we need to find n whose square is 32. We can say n as ‘5’ because 5 x 5 is lesser than or equal to 32. Now the quotient is 5 after subtracting 32-25 the remainder is 7.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number, 5 + 5, and we get 10, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 10n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 10n × n ≤ 700. Let us consider n as 7, now 107 x 7 = 749.

Step 6: Since 749 is greater than 700, we try with n = 6. We get 106 x 6 = 636.

Step 7: Subtract 700 from 636, and the difference is 64.

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 6400.

Step 9: Now we need to find the new divisor that is 113 because 1136 x 6 = 6816.

Step 10: Subtracting 6816 from 6400, we get the result 584.

Step 11: Now the quotient is 56.6.

Step 12: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue till the remainder is zero.

So the square root of √3200 ≈ 56.568.