Square Root of 3425
2026-02-28 12:58 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3425

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 3425, we need to group it as 34 and 25.

Step 2: Now we need to find n whose square is less than or equal to 34. We can say n is ‘5’ because 5 x 5 = 25 is less than 34. Now the quotient is 5 after subtracting 25 from 34; the remainder is 9.

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 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 ≤ 925. Let us consider n as 9, now 10 x 9 x 9 = 810.

Step 6: Subtract 925 from 810; the difference is 115, and the quotient is 59.

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 11500.

Step 8: Now we need to find the new divisor that is 585 because 585 x 9 = 5265.

Step 9: Subtracting 5265 from 11500, we get the result 6235.

Step 10: Now the quotient is 58.5.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero. So the square root of √3425 is approximately 58.51.