Square Root of 7825
2026-02-28 01:37 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-7825

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 7825, we group it as 78 and 25.

Step 2: Now we need to find n whose square is 64. We can say n as ‘8’ because 8 x 8 is lesser than or equal to 78. Now the quotient is 8 after subtracting 64 from 78, the remainder is 14

Step 3: Now let us bring down 25 which is the new dividend. Add the old divisor with the same number 8 + 8 we get 16 which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 16n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 16n x n ≤ 1425. Let us consider n as 8, now 16 x 8 + 8 = 136 Step 6: Subtract 136 from 1425, the difference is 89, and the quotient is 88.

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 zeros to the dividend. Now the new dividend is 8900.

Step 8: Now we need to find the new divisor that is 883 because 883 x 10 = 8830.

Step 9: Subtracting 8830 from 8900 we get the result 70.

Step 10: Now the quotient is 88.4.

Step 11: 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 √7825 ≈ 88.44.