Find the square root of 841 by division method?

To find the square root of 841 using the division method, we can break it down into a series of logical steps. This method is particularly useful for larger numbers and involves a systematic approach to arrive at the square root.

Step-by-Step Process

Step 1: Set Up the Number

First, we write the number 841 in pairs, starting from the right. Since 841 has three digits, we can group it as follows:

• 8 | 41

Step 2: Find the Largest Square

Next, we need to find the largest square number that is less than or equal to the leftmost pair (which is 8 in this case). The largest square less than or equal to 8 is 2, since:

• 2 x 2 = 4

We write 2 above the line, which represents the first digit of the square root.

Step 3: Subtract and Bring Down

Now, we subtract 4 from 8:

• 8 - 4 = 4

Next, we bring down the next pair (41), making it 441.

Step 4: Double the Quotient

We now double the quotient we found (which is 2) to get 4. This will help us find the next digit of the square root:

• 4 (double of 2)

Step 5: Find the Next Digit

We need to find a digit (let's call it 'x') such that:

• (40 + x) x ≤ 441

Testing with different digits, we find that:

• 41 x 1 = 41
• 42 x 2 = 84
• 43 x 3 = 129
• 44 x 4 = 176
• 45 x 5 = 225
• 46 x 6 = 276
• 47 x 7 = 329
• 48 x 8 = 384
• 49 x 9 = 441

Here, we see that 49 x 9 = 441 is exactly equal to 441. So, we write 9 above the line next to 2, making the square root so far 29.

Step 6: Final Calculation

Now, we subtract 441 from 441:

• 441 - 441 = 0

Since there is no remainder, we have found that the square root of 841 is 29.

Summary

The square root of 841, calculated using the division method, is 29. This method is effective for finding square roots of larger numbers and helps in understanding the relationship between squares and their roots.