Square Root of 3225
2026-02-28 12:42 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3225

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 3225, we need to group it as 32 and 25.

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

Step 3: Now let us bring down 25 which is the new dividend. Add the old divisor with the same number 5 + 5 to get 10, which will be our new divisor.

Step 4: The new divisor will be 10n. We need to find the value of n such that 10n x n ≤ 725. Let us consider n as 7, now 107 x 7 = 749, which is more than 725, so n should be less than 7.

Step 5: If n = 6, then 106 x 6 = 636, which fits. Subtracting gives a remainder of 89.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point and add two zeroes to the dividend. Now the new dividend is 8900.

Step 7: Now we need to find the new divisor. Extend the divisor to 1066 and find n such that 1066n x n is close to 8900. Let n = 8, then 10668 x 8 = 85344, which is an overestimate, thus n should be less than 8.

Step 8: Try n = 7, then 10667 x 7 = 74669, which fits. Subtracting gives a remainder of 1431.

Step 9: Continue doing these steps until we get two numbers after the decimal point. For example, the result will approximate to 56.77. So the square root of √3225 is approximately 56.77.