Square Root of 729 (√729)

Square Root of 729

Here we will define, analyze, simplify, and calculate the square root of 729. We start off with the definition and then answer some common questions about the square root of 729. Then, we will show you different ways of calculating the square root of 729 with and without a computer or calculator. We have a lot of information to share, so let's get started!

Square root of 729 definition
The square root of 729 in mathematical form is written with the radical sign like this √729. We call this the square root of 729 in radical form. The square root of 729 is a quantity (q) that when multiplied by itself will equal 729.

√729 = q × q = q²

Is 729 a perfect square?
729 is a perfect square if the square root of 729 equals a whole number. As we have calculated further down on this page, the square root of 729 is a whole number.

729 is a perfect square.

Is the square root of 729 rational or irrational?
The square root of 729 is a rational number if 729 is a perfect square. It is an irrational number if it is not a perfect square. Since 729 is a perfect square, it is rational number. This means that the answer to "the square root of 729?" will have no decimals.

√729 is a rational number

Can the square root of 729 be simplified?
A square root of a perfect square can be simplified because the square root of a perfect square will equal a whole number:

√729 = 27

How to calculate the square root of 729 with a calculator
The easiest and most boring way to calculate the square root of 729 is to use your calculator! Simply type in 729 followed by √x to get the answer. We did that with our calculator and got the following answer:

√729 = 27

How to calculate the square root of 729 with a computer
If you are using a computer that has Excel or Numbers, then you can enter SQRT(729) in a cell to get the square root of 729. Below is the result we got:

SQRT(729) = 27

What is the square root of 729 written with an exponent?
All square roots can be converted to a number (base) with a fractional exponent. The square root of 729 is no exception. Here is the rule and the answer to "the square root of 729 converted to a base with an exponent?":

√b = b^½

√729 = 729^½

How to find the square root of 729 by long division method
Here we will show you how to calculate the square root of 729 using the long division method. This is the lost art of how they calculated the square root of 729 by hand before modern technology was invented.

Step 1)
Set up 729 in pairs of two digits from right to left:

Step 2)
Starting with the first set: the largest perfect square less than or equal to 7 is 4, and the square root of 4 is 2. Therefore, put 2 on top and 4 at the bottom like this:

2
07	29
4

Step 3)
Calculate 7 minus 4 and put the difference below. Then move down the next set of numbers.

2
07	29
4
3	29

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

4? × ? ≤ 329

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:

47 × 7 = 329.

Now, enter 7 on top, and 329 at the bottom:

2	7
07	29
4
3	29
3	29

The difference between the bottom two numbers is zero, therefore, you are done! The answer is the green numbers on top. Once again, the square root of 729 is 27.

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 729 on this page.

Notes
Remember that negative times negative equals positive. Thus, the square root of 729 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 730
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