Question

square root of 232 by long division method​

Answer 1

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Answer 2

Here we will show you how to calculate the square root of 232 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 232 by hand before modern technology was invented.

Step 1)
Set up 232 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:

2 32 00


Step 2)
Starting with the first set: the largest perfect square less than or equal to 2 is 1, and the square root of 1 is 1. Therefore, put 1 on top and 1 at the bottom like this:

1
2 32 00
1


Step 3)
Calculate 2 minus 1 and put the difference below. Then move down the next set of numbers.

1
2 32 00
1
1 32


Step 4)
Double the number in green on top: 1 × 2 = 2. Then, use 2 and the bottom number to make this problem:

2? × ? ≤ 132

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 5. Replace the question marks in the problem with 5 to get:

25 × 5 = 125.

Now, enter 5 on top, and 125 at the bottom:

1 5
2 32 00
1
1 32
1 25


Step 5)
Calculate 132 minus 125 and put the difference below. Then move down the next set of numbers.

1 5
2 32 00
1
1 32
1 25
0 07 00


Step 6)
Double the number in green on top: 15 × 2 = 30. Then, use 30 and the bottom number to make this problem:

30? × ? ≤ 700

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 2. Now, enter 2 on top:

1 5 2
2 32 00
1
1 32
1 25
0 07 00

That's it! The answer is on top. The square root of 232 with one digit decimal accuracy is 15.2. Did you notice that the last two steps repeat the previous two steps. You can add decimals by simply adding more sets of 00 and repeating the last two steps over and over.