Square Root of 361 (√361)

Square Root of 361

Here we will define, analyze, simplify, and calculate the square root of 361. We start off with the definition and then answer some common questions about the square root of 361. Then, we will show you different ways of calculating the square root of 361 with and without a computer or calculator. We have a lot of information to share, so let's get started!

Square root of 361 definition
The square root of 361 in mathematical form is written with the radical sign like this √361. We call this the square root of 361 in radical form. The square root of 361 is a quantity (q) that when multiplied by itself will equal 361.

√361 = q × q = q²

Is 361 a perfect square?
361 is a perfect square if the square root of 361 equals a whole number. As we have calculated further down on this page, the square root of 361 is a whole number.

361 is a perfect square.

Is the square root of 361 rational or irrational?
The square root of 361 is a rational number if 361 is a perfect square. It is an irrational number if it is not a perfect square. Since 361 is a perfect square, it is rational number. This means that the answer to "the square root of 361?" will have no decimals.

√361 is a rational number

Can the square root of 361 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:

√361 = 19

How to calculate the square root of 361 with a calculator
The easiest and most boring way to calculate the square root of 361 is to use your calculator! Simply type in 361 followed by √x to get the answer. We did that with our calculator and got the following answer:

√361 = 19

How to calculate the square root of 361 with a computer
If you are using a computer that has Excel or Numbers, then you can enter SQRT(361) in a cell to get the square root of 361. Below is the result we got:

SQRT(361) = 19

What is the square root of 361 written with an exponent?
All square roots can be converted to a number (base) with a fractional exponent. The square root of 361 is no exception. Here is the rule and the answer to "the square root of 361 converted to a base with an exponent?":

√b = b^½

√361 = 361^½

How to find the square root of 361 by long division method
Here we will show you how to calculate the square root of 361 using the long division method. This is the lost art of how they calculated the square root of 361 by hand before modern technology was invented.

Step 1)
Set up 361 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 3 is 1, and the square root of 1 is 1. Therefore, put 1 on top and 1 at the bottom like this:

1
03	61
1

Step 3)
Calculate 3 minus 1 and put the difference below. Then move down the next set of numbers.

1
03	61
1
2	61

Step 4)
Double the number in green on top: 1 × 2 = 2. Then, use 2 and the bottom number to make this problem:

2? × ? ≤ 261

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:

29 × 9 = 261.

Now, enter 9 on top, and 261 at the bottom:

1	9
03	61
1
2	61
2	61

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 361 is 19.

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 361 on this page.

Notes
Remember that negative times negative equals positive. Thus, the square root of 361 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 362
Here is the next number on our list that we have equally detailed square root information about.