find the square root of the following numbers by prime factorization method of 4094
Answers
Answer:
10th: √4094 ≈ 64.0
100th: √4094 ≈ 63.98
1000th: √4094 ≈ 63.984
What is the square root of 4094 as a fraction?
Like we said above, since the square root of 4094 is an irrational number, we cannot make it into an exact fraction. However, we can make it into an approximate fraction using the square root of 4094 rounded to the nearest hundredth.
√4094
≈ 63.98/1
≈ 6398/100
≈ 63 49/50
What is the square root of 4094 written with an exponent?
All square roots can be converted to a number (base) with a fractional exponent. The square root of 4094 is no exception. Here is the rule and the answer to "the square root of 4094 converted to a base with an exponent?":
√b = b½
√4094 = 4094½
How to find the square root of 4094 by long division method
Here we will show you how to calculate the square root of 4094 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 4094 by hand before modern technology was invented.
Step 1)
Set up 4094 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
40 94 00
Step 2)
Starting with the first set: the largest perfect square less than or equal to 40 is 36, and the square root of 36 is 6. Therefore, put 6 on top and 36 at the bottom like this:
6
40 94 00
36
Step 3)
Calculate 40 minus 36 and put the difference below. Then move down the next set of numbers.
6
40 94 00
36
4 94
Step 4)
Double the number in green on top: 6 × 2 = 12. Then, use 12 and the bottom number to make this problem:
12? × ? ≤ 494
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 3. Replace the question marks in the problem with 3 to get:
123 × 3 = 369.
Now, enter 3 on top, and 369 at the bottom:
6 3
40 94 00
36
4 94
3 69
Step 5)
Calculate 494 minus 369 and put the difference below. Then move down the next set of numbers.
6 3
40 94 00
36
4 94
3 69
1 25 00
Step 6)
Double the number in green on top: 63 × 2 = 126. Then, use 126 and the bottom number to make this problem:
126? × ? ≤ 12500
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 9. Now, enter 9 on top:
6 3 9
40 94 00
36
4 94
3 69
1 25 00
That's it! The answer is on top. The square root of 4094 with one digit decimal accuracy is 63.9. 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.
Square Root of a Number
Please enter another number in the box below to get the square root of the number and other detailed information like you got for 4094 on this page.
Notes
Remember that negative times negative equals positive. Thus, the square root of 4094 does not only have the positive answer that we have explained above, but also the negative counterpart.