## How to use the SQRT function

**What is the SQRT function?**

The SQRT function calculates the positive square root.

**What is a square root?**

The square root of x is denoted by √x but it can also be x^{1/2} or x^{0.5} A square root of a number x is a value that when multiplied by itself equals x.

√x * √x = x

For example

√4 * √4 = 4

It is the reverse operation of squaring a number.

x^{2} = 4

x = √4

x_{1} = +2

x_{2} = -2

**Why are there two solutions to a square root?**

There are two solutions to a square root is because when you square a number whether it is positive or negative you get the same result.

For example, (-2)^{2} = 2^{2} = 4.

If you want to find the number that was squared to get 4, you have two possible answers:

√4 = 2 or √4 = -2.

Often we only want the positive solution of a square root, like when we are dealing with length, area, or time.

**Is there a solution to a square root of a negative number?**

No, there is no real number solution for the square root of a negative number. For example: √(-16) has no solution because if you square a real number you always get a positive result:

(-4)2 = 16

4^2 = 16

So no real number squared can produce a negative result.

However, we can find a complex number solution by introducing the imaginary unit i:

i = √(-1)

Where i is defined such that i^{2} = -1. Using i we can take square roots of negatives:

√(-16) = 4i

Because (4i)(4i) = 16*i^{2 }= 16*-1 = -16

Square roots of negative real numbers are undefined, the concept of imaginary numbers and the imaginary unit i allows extending square roots to negative and complex numbers.

Check out the Engineering category for Excel functions dealing with complex numbers involving imaginary units.

**What is an even power?**

An even power or exponent refers to when a number is raised to an even integer exponent. Even powers have the general form x^{2n} where n is some integer.

The first even power is the square x^{2}. Higher even powers are x^{2}, x^{4}, x^{6}, etc.

**What is an even number?**

An even number is an integer (whole number) that is divisible by 2 with no remainder.

### SQRT Function Syntax

SQRT(*number*)

### SQRT Function Arguments

number |
Required. The positive numerical value for which you want the square root. |

### Comments

Use the ABS function to remove the sign if a number is negative.

Recommended articles

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### SQRT Function example

Formula in cell C3:

### Functions in 'Math and trigonometry' category

The SQRT function function is one of many functions in the 'Math and trigonometry' category.

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