Question

Square root of 1042441 by division method

Answer 1

To find the square root of 1042441 using the division method, we can follow these steps:

1. Start by grouping the digits of the number into pairs from right to left. In this case, we have 10, 42, 44, and 1.

2. Find the largest digit that, when squared, is less than or equal to the first pair of digits (10). In this case, the largest digit is 3 because 3 squared is 9.

3. Write down 3 as the first digit of the square root.

4. Multiply the first digit (3) by 2 and write it as the divisor. Place a blank space for the quotient.

5. Perform long division by dividing the first pair of digits (10) by the divisor (6). The quotient is 1 and the remainder is 4. Write down the quotient above the blank space.

6. Bring down the next pair of digits (42) and place it next to the remainder (4). The new dividend is 442.

7. Double the current digit of the square root (3) and write it as the new divisor. Place a blank space for the quotient.

8. Perform long division by dividing the new dividend (442) by the new divisor (6). The quotient is 73 and the remainder is 4. Write down the quotient above the blank space.

9. Repeat steps 6-8 for the remaining pairs of digits until all pairs have been included.

10. The final quotient obtained is the square root of the given number. In this case, the square root of 1042441 is approximately 1021.

Therefore, the square root of 1042441 by the division method is approximately 1021.

real

Answer 2

1021

Explanation:

Step 1: Begin by separating the digits of the number into pairs, starting from the right. In this case, we have 1, 04, 24, and 41.

Step 2: Find the largest number whose square is less than or equal to the leftmost pair, which is 1. In this case, the largest number whose square is less than or equal to 1 is 1 itself.

Step 3: Write down the number found in step 2 as the first digit of the square root. In this case, the first digit is 1.

Step 4: Divide the first pair (1) by the first digit (1), which gives us 1. Write this quotient below the first pair.

Step 5: Multiply the divisor (1) by the quotient (1) and subtract the result (1) from the first pair (1). We get 0 as the difference.

Step 6: Bring down the next pair (04) to the right of the difference (0).

Step 7: Multiply the quotient (1) by 2 and write the result (2) below the difference.

Step 8: Add the last digit of the result from step 7 (2) to the quotient (1) to get 3 as the new digit to bring down.

Step 9: Repeat steps 4 to 8 until all the pairs have been processed.

Step 10: Continue this process until you have reached the desired level of accuracy or until the calculation becomes too long.

Following these steps, we can find that the square root of 1042441 is approximately 1021.

Hope this helps!