Square Root of 6741


Square Root of 6741

Here we will define, analyze, simplify, and calculate the square root of 6741. We start off with the definition and then answer some common questions about the square root of 6741. Then, we will show you different ways of calculating the square root of 6741 with and without a computer or calculator. We have a lot of information to share, so let's get started!



Square root of 6741 definition
The square root of 6741 in mathematical form is written with the radical sign like this √6741. We call this the square root of 6741 in radical form. The square root of 6741 is a quantity (q) that when multiplied by itself will equal 6741.

6741 = q × q = q2



Is 6741 a perfect square?
6741 is a perfect square if the square root of 6741 equals a whole number. As we have calculated further down on this page, the square root of 6741 is not a whole number.

6741 is not a perfect square.



Is the square root of 6741 rational or irrational?
The square root of 6741 is a rational number if 6741 is a perfect square. It is an irrational number if it is not a perfect square. Since 6741 is not a perfect square, it is an irrational number. This means that the answer to "the square root of 6741?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.

6741 is an irrational number



Can the square root of 6741 be simplified?
You can simplify 6741 if you can make 6741 inside the radical smaller. We call this process "to simplify a surd". The square root of 6741 can be simplified.

6741 = 3√749



How to calculate the square root of 6741 with a calculator
The easiest and most boring way to calculate the square root of 6741 is to use your calculator! Simply type in 6741 followed by √x to get the answer. We did that with our calculator and got the following answer with 9 decimal numbers:

6741 ≈ 82.103593100




How to calculate the square root of 6741 with a computer
If you are using a computer that has Excel or Numbers, then you can enter SQRT(6741) in a cell to get the square root of 6741. Below is the result we got with 13 decimals. We call this the square root of 6741 in decimal form.

SQRT(6741) ≈ 82.1035931004240



What is the square root of 6741 rounded?
The square root of 6741 rounded to the nearest tenth, means that you want one digit after the decimal point. The square root of 6741 rounded to the nearest hundredth, means that you want two digits after the decimal point. The square root of 6741 rounded to the nearest thousandth, means that you want three digits after the decimal point.

10th: √6741 ≈ 82.1

100th: √6741 ≈ 82.10

1000th: √6741 ≈ 82.104



What is the square root of 6741 as a fraction?
Like we said above, since the square root of 6741 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 6741 rounded to the nearest hundredth.

6741
≈ 82.10/1
≈ 8210/100
≈ 82 1/10



What is the square root of 6741 written with an exponent?
All square roots can be converted to a number (base) with a fractional exponent. The square root of 6741 is no exception. Here is the rule and the answer to "the square root of 6741 converted to a base with an exponent?":

b = b½

6741 = 6741½



How to find the square root of 6741 by long division method
Here we will show you how to calculate the square root of 6741 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 6741 by hand before modern technology was invented.

Step 1)
Set up 6741 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:

674100



Step 2)
Starting with the first set: the largest perfect square less than or equal to 67 is 64, and the square root of 64 is 8. Therefore, put 8 on top and 64 at the bottom like this:

8
674100
64



Step 3)
Calculate 67 minus 64 and put the difference below. Then move down the next set of numbers.

8
674100
64
341



Step 4)
Double the number in green on top: 8 × 2 = 16. Then, use 16 and the bottom number to make this problem:

16? × ? ≤ 341

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 2. Replace the question marks in the problem with 2 to get:

162 × 2 = 324.

Now, enter 2 on top, and 324 at the bottom:

82
674100
64
341
324



Step 5)
Calculate 341 minus 324 and put the difference below. Then move down the next set of numbers.

82
674100
64
341
324
01700



Step 6)
Double the number in green on top: 82 × 2 = 164. Then, use 164 and the bottom number to make this problem:

164? × ? ≤ 1700

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 1. Now, enter 1 on top:

821
674100
64
341
324
01700

That's it! The answer is on top. The square root of 6741 with one digit decimal accuracy is 82.1. 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 6741 on this page.






Notes
Remember that negative times negative equals positive. Thus, the square root of 6741 does not only have the positive answer that we have explained above, but also the negative counterpart.

We often refer to perfect square roots on this page. You may want to use the list of perfect squares for reference.


Square Root of 6742
Here is the next number on our list that we have equally detailed square root information about.


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