Square Root of 400 (√400)

Square Root of 400

Here we will define, analyze, simplify, and calculate the square root of 400. We start off with the definition and then answer some common questions about the square root of 400. Then, we will show you different ways of calculating the square root of 400 with and without a computer or calculator. We have a lot of information to share, so let's get started!

Square root of 400 definition
The square root of 400 in mathematical form is written with the radical sign like this √400. We call this the square root of 400 in radical form. The square root of 400 is a quantity (q) that when multiplied by itself will equal 400.

√400 = q × q = q²

Is 400 a perfect square?
400 is a perfect square if the square root of 400 equals a whole number. As we have calculated further down on this page, the square root of 400 is a whole number.

400 is a perfect square.

Is the square root of 400 rational or irrational?
The square root of 400 is a rational number if 400 is a perfect square. It is an irrational number if it is not a perfect square. Since 400 is a perfect square, it is rational number. This means that the answer to "the square root of 400?" will have no decimals.

√400 is a rational number

Can the square root of 400 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:

√400 = 20

How to calculate the square root of 400 with a calculator
The easiest and most boring way to calculate the square root of 400 is to use your calculator! Simply type in 400 followed by √x to get the answer. We did that with our calculator and got the following answer:

√400 = 20

How to calculate the square root of 400 with a computer
If you are using a computer that has Excel or Numbers, then you can enter SQRT(400) in a cell to get the square root of 400. Below is the result we got:

SQRT(400) = 20

What is the square root of 400 written with an exponent?
All square roots can be converted to a number (base) with a fractional exponent. The square root of 400 is no exception. Here is the rule and the answer to "the square root of 400 converted to a base with an exponent?":

√b = b^½

√400 = 400^½

How to find the square root of 400 by long division method
Here we will show you how to calculate the square root of 400 using the long division method. This is the lost art of how they calculated the square root of 400 by hand before modern technology was invented.

Step 1)
Set up 400 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 4 is 4, and the square root of 4 is 2. Therefore, put 2 on top and 4 at the bottom like this:

2
04	00
4

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

2
04	00
4
0	00

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

4? × ? ≤ 0

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 0. Replace the question marks in the problem with 0 to get:

40 × 0 = 0.

Now, enter 0 on top, and 0 at the bottom:

2	0
04	00
4
0	00
0	00

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 400 is 20.

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 400 on this page.

Notes
Remember that negative times negative equals positive. Thus, the square root of 400 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 401
Here is the next number on our list that we have equally detailed square root information about.