Square Root of 888
2026-02-21 20:55 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-888

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 888, we need to group it as 88 and 8.

Step 2: Now we need to find a number 'n' whose square is 8 or less. We can say n is ‘2’ because 2 x 2 = 4, which is less than 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.

Step 3: Now let us bring down 88, 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 the sum of the dividend and quotient. Now we get 4n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 488. Let's consider n as 7; now 4 x 7 x 7 = 196.

Step 6: Subtract 196 from 488; the difference is 292, and the quotient is 27.

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 29200.

Step 8: Now we need to find the new divisor that is 279 because 2799 x 9 = 25191.

Step 9: Subtracting 25191 from 29200, we get the result 4009.

Step 10: Now the quotient is 29.7.

Step 11: Continue 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 √888 is approximately 29.79.