Square Root of 850
2026-02-28 11:37 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-850

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 850, we need to group it as 50 and 8.

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

Step 3: Now let us bring down 50, 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 4n. We need to find the value of n such that 4n x n ≤ 450. Let us consider n as 9, now 49 x 9 = 441.

Step 5: Subtract 441 from 450; the difference is 9, and the quotient is 29.

Step 6: Since the new 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 900.

Step 7: Now we need to find the new divisor that is 581, because 581 x 1 = 581.

Step 8: Subtracting 581 from 900, we get the result 319.

Step 9: Now the quotient is 29.1.

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

So the square root of √850 is approximately 29.15.