Square Root of 6625
2026-02-28 14:04 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-6625

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 6625, we need to group it as 65 and 6.

Step 2: Now we need to find n whose square is less than or equal to 6. We can say n as '2' because 2 x 2 is 4, which is less than 6. Now the quotient is 2, and after subtracting 4 from 6, the remainder is 2.

Step 3: Now let us bring down 625, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 2625.

Step 5: The next step is finding 4n x n ≤ 2625. Let us consider n as 6; now, 46 x 6 = 276.

Step 6: Subtract 276 from 2625, and the difference is 2349. The new quotient is 26.

Step 7: Since the dividend is less than the new product, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 234900.

Step 8: Now we need to find the new number n, such that 526n x n is close to 234900. Let's assume n = 4. Then 5264 x 4 ≈ 21056.

Step 9: Subtracting 21056 from 234900, we get the result 22444.

Step 10: Now the quotient is 81.4.

Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √6625 ≈ 81.41.