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For most school mathematics, negative numbers do not have square roots. This is because a negative number multiplied by itself is a negative times a negative and so is positive.
When (if) you study advanced mathematics, you will learn that there is a solution and this falls within the realms of complex mathematics and imaginary numbers.
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How can there be a square root of a negative number?
Square roots of negative numbers are what are called imaginary numbers. The building block of imaginary numbers is the symbol i which is defined as the square root of negative 1. The square root of other negative numbers can be expressed using i. For example, the square root of negative sixteen is 4i, the square root of negative nine is 3i and so on.
How many square roots do negative numbers have?
Negative numbers do not have "real number" square roots.However, they will have two roots (when using imaginary numbers) as do other numbers, where a root including i(square root of -1) is positive or negative.
Why is it possible to find a real cube root of a negative number but not a real square root of a negative number?
You cannot get real square root of a negative number because two numbers multiplied by themselves are always positive You can always get a real cube root of a negative number because three negative numbers multiplied by themselves give a negative .
What can you not do with square root?
When dealing with real numbers, you cannot take the square root of a negative number. The concept of the imaginary number was created to handle the square root of a negative number.That's almost like saying "when dealing with numbers bigger than 10, you cannot take the square root of 4. If what you are dealing with does not represent a number, then you cannot find its square root.
What does I mean in square root -1?
The square of any real number is non-negative. For example (-3)2 = +9 So, no real number can have a negative square root. Occasionally, though, mathematicians come across the need to find the square root of a negative number (for example in solving some quadratic equations). So they invented a family of numbers called imaginary numbers and the i (lower case) stands for the imaginary square root of -1. Apart from having a negative square, they are just like "ordinary" real numbers.
