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.

x² = 4
x = √4
x₁ = +2
x₂ = -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 = 2² = 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 i² = -1. Using i we can take square roots of negatives:

√(-16) = 4i

Because (4i)(4i) = 16*i² = 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 x²ⁿ where n is some integer.
The first even power is the square x². Higher even powers are x², x⁴, x⁶, 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

Comments

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

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