How to find theSquare root of 965
Answers
Answer :
- √965 = q × q = q2
- √965 ≈ 31.064449134
- 10th: √965 ≈ 31.1
- 100th: √965 ≈ 31.06
- 1000th: √965 ≈ 31.064
The square root of 965 with one digit decimal accuracy is 31.0.
Step-by-step explanation:
Here we will show you how to calculate the square root of 965 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 965 by hand before modern technology was invented.
Step 1)
Set up 965 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
9 65 00
Step 2)
Starting with the first set: the largest perfect square less than or equal to 9 is 9, and the square root of 9 is 3. Therefore, put 3 on top and 9 at the bottom like this:
3
9 65 00
9
Step 3)
Calculate 9 minus 9 and put the difference below. Then move down the next set of numbers.
3
9 65 00
9
0 65
Step 4)
Double the number in green on top: 3 × 2 = 6. Then, use 6 and the bottom number to make this problem:
6? × ? ≤ 65
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 1. Replace the question marks in the problem with 1 to get:
61 × 1 = 61.
Now, enter 1 on top, and 61 at the bottom:
3 1
9 65 00
9
0 65
0 61
Step 5)
Calculate 65 minus 61 and put the difference below. Then move down the next set of numbers.
3 1
9 65 00
9
0 65
0 61
0 04 00
Step 6)
Double the number in green on top: 31 × 2 = 62. Then, use 62 and the bottom number to make this problem:
62? × ? ≤ 400
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:
3 1 0
9 65 00
9
0 65
0 61
0 04 00
That's it! The answer is on top. The square root of 965 with one digit decimal accuracy is 31.0. 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