Here we will define, analyze, simplify, and calculate the square root of 1. We start off with the definition and then answer some common questions about the square root of 1. Then, we will show you different ways of calculating the square root of 1 with and without a computer or calculator. We have a lot of information to share, so let's get started!

**Square root of 1 definition**

The square root of 1 in mathematical form is written with the radical sign like this √1. We call this the square root of 1 in radical form. The square root of 1 is a quantity (q) that when multiplied by itself will equal 1.

√1 = q × q = q

^{2}

**Is 1 a perfect square?**

1 is a perfect square if the square root of 1 equals a whole number. As we have calculated further down on this page, the square root of 1 is a whole number.

1 is a perfect square.

**Is the square root of 1 rational or irrational?**

The square root of 1 is a rational number if 1 is a perfect square. It is an irrational number if it is not a perfect square. Since 1 is a perfect square, it is rational number. This means that the answer to "the square root of 1?" will have no decimals.

√1 is a rational number

**Can the square root of 1 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:

√1 = 1

**How to calculate the square root of 1 with a calculator**

The easiest and most boring way to calculate the square root of 1 is to use your calculator! Simply type in 1 followed by √x to get the answer. We did that with our calculator and got the following answer:

√1 = 1

**How to calculate the square root of 1 with a computer**

If you are using a computer that has Excel or Numbers, then you can enter SQRT(1) in a cell to get the square root of 1. Below is the result we got:

SQRT(1) = 1

**What is the square root of 1 written with an exponent?**

All square roots can be converted to a number (base) with a fractional exponent. The square root of 1 is no exception. Here is the rule and the answer to "the square root of 1 converted to a base with an exponent?":

√b = b

^{½}

√1 = 1

^{½}

**How to find the square root of 1 by long division method**

Here we will show you how to calculate the square root of 1 using the long division method. This is the lost art of how they calculated the square root of 1 by hand before modern technology was invented.

**Step 1)**

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

1 |

**Step 2)**

Starting with the first set: the largest perfect square less than or equal to 1 is 1, and the square root of 1 is 1. Therefore, put 1 on top and 1 at the bottom like this:

1 | ||||

1 | ||||

1 | ||||

The difference between the bottom two numbers is zero, therefore, you are done! The answer is the green number on top. Once again, the square root of 1 is 1.

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 1 on this page.

**Notes**

Remember that negative times negative equals positive. Thus, the square root of 1 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 2

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

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