square root by long division method 1767
Answers
Explanation:
Here we will show you how to calculate the square root of 1767 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 1767 by hand before modern technology was invented.
Step 1)
Set up 1767 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
17 67 00
Step 2)
Starting with the first set: the largest perfect square less than or equal to 17 is 16, and the square root of 16 is 4. Therefore, put 4 on top and 16 at the bottom like this:
4
17 67 00
16
Step 3)
Calculate 17 minus 16 and put the difference below. Then move down the next set of numbers.
4
17 67 00
16
1 67
Step 4)
Double the number in green on top: 4 × 2 = 8. Then, use 8 and the bottom number to make this problem:
8? × ? ≤ 167
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 2. Replace the question marks in the problem with 2 to get:
82 × 2 = 164.
Now, enter 2 on top, and 164 at the bottom:
4 2
17 67 00
16
1 67
1 64
Step 5)
Calculate 167 minus 164 and put the difference below. Then move down the next set of numbers.
4 2
17 67 00
16
1 67
1 64
0 03 00
Step 6)
Double the number in green on top: 42 × 2 = 84. Then, use 84 and the bottom number to make this problem:
84? × ? ≤ 300
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:
4 2 0
17 67 00
16
1 67
1 64
0 03 00
That's it! The answer is on top. The square root of 1767 with one digit decimal accuracy is 42.0. 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.
Answer:-
The square root of 1767 with one digit decimal accuracy is 42.0.
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