Find the square root of the following numbers using long division method. (iii) 3684
Answers
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Answer:
How to find the square root of 3684 by long division method
Here we will show you how to calculate the square root of 3684 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 3684 by hand before modern technology was invented.
Step 1)
Set up 3684 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
36 84 00
Step 2)
Starting with the first set: the largest perfect square less than or equal to 36 is 36, and the square root of 36 is 6. Therefore, put 6 on top and 36 at the bottom like this:
6
36 84 00
36
Step 3)
Calculate 36 minus 36 and put the difference below. Then move down the next set of numbers.
6
36 84 00
36
0 84
Step 4)
Double the number in green on top: 6 × 2 = 12. Then, use 12 and the bottom number to make this problem:
12? × ? ≤ 84
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:
120 × 0 = 0.
Now, enter 0 on top, and 0 at the bottom:
6 0
36 84 00
36
0 84
0 00
Step 5)
Calculate 84 minus 0 and put the difference below. Then move down the next set of numbers.
6 0
36 84 00
36
0 84
0 00
0 84 00
Step 6)
Double the number in green on top: 60 × 2 = 120. Then, use 120 and the bottom number to make this problem:
120? × ? ≤ 8400
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 6. Now, enter 6 on top:
6 0 6
36 84 00
36
0 84
0 00
0 84 00
That's it! The answer is on top. The square root of 3684 with one digit decimal accuracy is 60.6. 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