Square Root of 875
2026-02-28 11:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-875

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 875, we need to group it as 75 and 8.

Step 2: Now we need to find n whose square is 8. We can say n as ‘2’ because 2 x 2 is lesser than or equal to 8. Now the quotient is 2, after subtracting 8 - 4, the remainder is 4.

Step 3: Now let us bring down 75, which is the new dividend. Add the old divisor with the same number 2 + 2, we get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n × n ≤ 475. Let us consider n as 5, now 4 x 5 x 5 = 100

Step 6: Subtract 475 from 100, the difference is 375, and the quotient is 25.

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 37500.

Step 8: Now we need to find the new divisor that is 29 because 529 x 5 = 2645

Step 9: Subtracting 2645 from 37500, we get the result 11095.

Step 10: Now the quotient is 29.5

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √875 is 29.58.