# How to use the SQRT function

**What is the SQRT function?**

The SQRT function calculates the positive square root.

The SQRT function is not the only method to calculate the square root in an Excel formula. The caret symbol lets you raise a number to a given power, using 0.5 as a power is the same as the square root.

For example, SQRT(100) equals 10, however, 100^0.5 also equals 10.

The SQRT function can only calculate the square root, no other roots.

### Table of Contents

**What is a square root?**

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

âˆšx * âˆšx = x

For example

âˆš4 * âˆš4 = 4

It is the reverse operation of squaring a number.

x^{2} = 4

x = âˆš4

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:

âˆš4 = 2 or âˆš4 = -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:Â âˆš(-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 = âˆš(-1)

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

âˆš(-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.Â Even powers have the general form x^{2n}Â 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.

## 2. SQRT Function Syntax

SQRT(*number*)

## 3. SQRT Function Arguments

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

## 4. SQRT Function example

Formula in cell C3:

The first example in cell C2 and C3 demonstrates what you get if you try to square root a negative number in Excel. The formula returns the #NUM! error value if a number is negative.

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

Recommended articles

What is the ABS function? The ABS function converts negative numbers to positive numbers, in other words, the ABS function […]

The remaining example uses zero or positive numbers, the input numbers are in column B and the output is in column C.

## 5. Calculate the hypothenuse in a right triangle

The SQRT function lets you calculate the hypothenuse using the Pythagorean Theorem.

Excel formula in cell C5:

**What is the Pythagorean Theorem?**

The Pythagorean Theorem is a mathematical relationship that describes the lengths of the sides of a right triangle.

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

a^{2} + b^{2} = c^{2}

a and b are the lengths of the legs of the triangle.

c is the length of the hypotenuse.

To calculate the hypothenuse the formula becomes:

c = âˆš(a^{2} + b^{2})

### Explaining formula

#### Step 1 - Square leg 1

The caret character lets you raise a number to a given power. The caret symbol is only one character compared to the POWER function that also raises a number to a given power.

C2^2

becomes

6^2

and returns 36 (6 * 6 = 36).

#### Step 2 - Square leg 2

C3^2

becomes

8^2

and returns 64 (8 * 8 = 64).

#### Step 3 - Add the squared numbers

C2^2+C3^2

becomes

36 + 64 equals 100

#### Step 4 - Calculate the square root of the sum

SQRT(C2^2+C3^2)

becomes

SQRT(100)

and returns 10.

## 6. Calculate the legs (opposite and adjacent) in a right triangle

The SQRT function lets you calculate the legs of a right triangle using the Pythagorean Theorem.

Excel formula in cell C5:

**What is the Pythagorean Theorem?**

The Pythagorean Theorem is a mathematical relationship that describes the lengths of the sides of a right triangle.

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

a^{2} + b^{2} = c^{2}

a and b are the lengths of the legs of the triangle.

c is the length of the hypotenuse.

To calculate the leg of a right triangle the formula becomes:

a = âˆš(c^{2} - b^{2})

or

b = âˆš(c^{2} - a^{2})

### Explaining formula

#### Step 1 - Square the hypothenuse

The caret character lets you raise a number to a given power. The caret symbol is only one character compared to the POWER function that also raises a number to a given power.

C2^2

becomes

10^2

and returns 100 (10 * 10 = 100).

#### Step 2 - Square leg 2

C3^2

becomes

8^2

and returns 64 (8 * 8 = 64).

#### Step 3 - Subtract the squared hypothenuse with the squared leg 2

C2^2-C3^2

becomes

100 - 63 equals 36

#### Step 4 - Calculate the square root of the sum

SQRT(C2^2+C3^2)

becomes

SQRT(36)

and returns 6.

### Functions in 'Math and trigonometry' category

The SQRT function function is one of 73 functions in the 'Math and trigonometry' category.

## How to comment

How to add a formula to your comment<code>Insert your formula here.</code>

Convert less than and larger than signsUse html character entities instead of less than and larger than signs.

< becomes < and > becomes >

How to add VBA code to your comment[vb 1="vbnet" language=","]

Put your VBA code here.

[/vb]

How to add a picture to your comment:Upload picture to postimage.org or imgur

Paste image link to your comment.

Contact OscarYou can contact me through this contact form