Square Root of Negative 81 (√-81)

Square Root of Negative 81

So you want to calculate the square root of negative 81? In mathematical terms, you want the solution to the following:

√-81 = ?

If you enter SQRT(-81) into a spreadsheet on your computer, you will get an error message saying something like "argument must be greater or equal to 0" because the square root of negative 81 is not possible. There is no real number multiplied by itself that will equal -81.

However, it is possible to calculate the square root of negative 81 with a complex or imaginary square root number. We start by making the imaginary square root of negative 1. With this, we can combine real and imaginary square roots to make this true:

√-81 = √81 × √-1

The square root of 81 is 9. Furthermore, the square root of negative 1 is an imaginary insignificant number (iota) which can be transliterated as i. That's it. Now, we have our answer to the square root of negative 81:

√-81 = 9 i

Note: since negative times negative equals positive, one could therefore conclude that -9 i is also a correct answer to the square root of negative 81.

Square Root of a Negative Number
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Square Root of Negative 82
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