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Negative Square Roots

If we were to examine the title above we would realize it's inaccurate as there is no such thing as a negative square root among Real Numbers.

How is that possible? The definition of a square root is a number times itself. When you multiply number times itself you will always get a positive result. Example 2 x 2 = 4 and -2 x-2= 4

The square root of a negative number is referred to as an imaginary number as it does not exist as a Real Number. The imaginary number, i, is the square root of -1.

imaginary number i

When you square i, you will get -1.

A complex number is formed when you combine imaginary numbers with Real Numbers The form for complex numbers are a+bi.

How to simplify a negative square root?

Simplifying negative radicals is pretty much like simplifying any other radicals just filter out the √-1 and replace it with i.

Let’s give it a go:

example: square root of 15

-The number 36 is a perfect square and gets broken down to 6x6 so your answer would be

  • -  is explained as  x  or simply i

Still need help? Try using our square root calculator as a negative square root calculator to get your answer.