Square Root of 3500
2026-02-28 09:51 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3500

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 3500, we need to group it as 00 and 35.

Step 2: Now we need to find n whose square is less than or equal to 35. We can say n as ‘5’ because \(5 \times 5 = 25\) is lesser than or equal to 35. Now the quotient is 5, and after subtracting 25 from 35, the remainder is 10.

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

Step 4: The new divisor will be of the form 10n. Now we get 10n as the new divisor, we need to find the value of n.

Step 5: The next step is finding \(10n \times n \leq 1000\). Let us consider n as 9, now \(109 \times 9 = 981\).

Step 6: Subtract 981 from 1000, the difference is 19, 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 1900.

Step 8: Now we need to find the new divisor, which is 591 because \(591 \times 3 = 1773\).

Step 9: Subtracting 1773 from 1900, we get the result 127.

Step 10: Now the quotient is 59.3.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there is no decimal value; continue till the remainder is zero. So the square root of √3500 is approximately 59.16.