square root of 6322 by long division method
Answers
SQRT(6322) ≈ 79.5110055275369
the square root of 6322 using the long division method with one decimal place accuracy.
Step 1)
Set up 6322 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
63 22 00
Step 2)
Starting with the first set: the largest perfect square less than or equal to 63 is 49, and the square root of 49 is 7. Therefore, put 7 on top and 49 at the bottom like this:
7
63 22 00
49
Step 3)
Calculate 63 minus 49 and put the difference below. Then move down the next set of numbers.
7
63 22 00
49
14 22
Step 4)
Double the number in green on top: 7 × 2 = 14. Then, use 14 and the bottom number to make this problem:
14? × ? ≤ 1422
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 9. Replace the question marks in the problem with 9 to get:
149 × 9 = 1341.
Now, enter 9 on top, and 1341 at the bottom:
7 9
63 22 00
49
14 22
13
Step 5)
Calculate 1422 minus 1341 and put the difference below. Then move down the next set of numbers.
7 9
63 22 00
49
14 22
13 41
0 81 00
Step 6)
Double the number in green on top: 79 × 2 = 158. Then, use 158 and the bottom number to make this problem:
158? × ? ≤ 8100
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 5. Now, enter 5 on top:
7 9 5
63 22 00
49
14 22
13 41
0
That's it! The answer is on top. The square root of 6322 with one digit decimal accuracy is 79.5. 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.
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