find the square root of 9459 by long division method
Answers
Answer:
Here we will show you how to calculate the square root of 9459 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 9459 by hand before modern technology was invented.
Step 1)
Set up 9459 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
94 59 00
Step 2)
Starting with the first set: the largest perfect square less than or equal to 94 is 81, and the square root of 81 is 9. Therefore, put 9 on top and 81 at the bottom like this:
9
94 59 00
81
Step 3)
Calculate 94 minus 81 and put the difference below. Then move down the next set of numbers.
9
94 59 00
81
13 59
Step 4)
Double the number in green on top: 9 × 2 = 18. Then, use 18 and the bottom number to make this problem:
18? × ? ≤ 1359
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 7. Replace the question marks in the problem with 7 to get:
187 × 7 = 1309.
Now, enter 7 on top, and 1309 at the bottom:
9 7
94 59 00
81
13 59
13 09
Step 5)
Calculate 1359 minus 1309 and put the difference below. Then move down the next set of numbers.
9 7
94 59 00
81
13 59
13 09
0 50 00
Step 6)
Double the number in green on top: 97 × 2 = 194. Then, use 194 and the bottom number to make this problem:
194? × ? ≤ 5000
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:
9 7 2
94 59 00
81
13 59
13 09
0 50 00
That's it! The answer is on top. The square root of 9459 with one digit decimal accuracy is 97.2. 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.