Square Root of 798
2026-02-28 10:59 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-798

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 798, we need to group it as 98 and 7.

Step 2: Now we need to find n whose square is less than or equal to 7. We can say n as ‘2’ because 2² = 4 is lesser than or equal to 7. Now the quotient is 2, and after subtracting 4 from 7, the remainder is 3.

Step 3: Now let us bring down 98, which is the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.

Step 4: The new divisor will be 4n, and we need to find the value of n such that 4n × n ≤ 398.

Step 5: The next step is finding 4n × n ≤ 398. Let us consider n as 7, now 47 × 7 = 329.

Step 6: Subtract 329 from 398; the difference is 69, 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 6900.

Step 8: Now we need to find the new divisor that is 545 because 545 × 5 = 2725.

Step 9: Subtracting 2725 from 6900, we get the result 4175.

Step 10: Now the quotient is 28.2

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 √798 is approximately 28.25.