Square Root of 2042
2026-02-28 08:40 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2042

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 2042, we need to group it as 42 and 20.

Step 2: Now we need to find n whose square is less than or equal to 20. We can choose n as 4 because 4 x 4 = 16, which is less than 20. Now the quotient is 4, and after subtracting 16 from 20, the remainder is 4.

Step 3: Bring down 42, making the new dividend 442.

Step 4: Double the divisor, which was 4, to get 8. Now find a digit x such that 8x × x is less than or equal to 442. The closest value is 85, where 85 x 5 = 425.

Step 5: Subtract 425 from 442 to get 17, and the quotient is 45.

Step 6: 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, making it 1700.

Step 7: Double the current quotient and add it to the current divisor to get a new divisor, which becomes 905. Find a digit, let's say 1, such that 9051 x 1 is less than or equal to 1700.

Step 8: Continue this process to achieve the desired decimal places.

The approximate square root of 2042 is 45.179.