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 x1/2 or x0.5 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
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.
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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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