Square Root of 890
2026-02-28 10:03 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-890

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 890, we need to group it as 90 and 8.

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

Step 3: Now let us bring down 90, 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.

Step 5: The next step is finding 4n x n ≤ 490. Let us consider n as 9. Now 49 x 9 = 441.

Step 6: Subtract 490 from 441; the difference is 49, and the quotient is 29.

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 4900.

Step 8: Now we need to find the new divisor, which is 598, because 598 x 8 = 4784.

Step 9: Subtracting 4784 from 4900, we get the result 116. Step 10: Now the quotient is 29.8

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 √890 is approximately 29.83.