Question

find square root of 404 by division method
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Answer 1

Step 1)

Set up 404 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:

4 04 00

Step 2)

Starting with the first set: the largest perfect square less than or equal to 4 is 4, and the square root of 4 is 2. Therefore, put 2 on top and 4 at the bottom like this:

2

4 04 00

4

Step 3)

Calculate 4 minus 4 and put the difference below. Then move down the next set of numbers.

2

4 04 00

4

0 04

Step 4)

Double the number in green on top: 2 × 2 = 4. Then, use 4 and the bottom number to make this problem:

4? × ? ≤ 4

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 0. Replace the question marks in the problem with 0 to get:

40 × 0 = 0.

Now, enter 0 on top, and 0 at the bottom:

2 0

4 04 00

4

0 04

0 00

Step 5)

Calculate 4 minus 0 and put the difference below. Then move down the next set of numbers.

2 0

4 04 00

4

0 04

0 00

0 04 00

Step 6)

Double the number in green on top: 20 × 2 = 40. Then, use 40 and the bottom number to make this problem:

40? × ? ≤ 400

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 0. Now, enter 0 on top:

2 0 0

4 04 00

4

0 04

0 00

0 04 00

That's it! The answer is on top. The square root of 404 with one digit decimal accuracy is 20.0