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The square root of any negative number will always be a complex number.
The word 'complex' can be supplemented for the word 'imaginary' which is what they can sometimes be called.
'i' stands for imaginary and equals the square root of minus one.
sq(-1) = i - (that is the basic fact)
The imaginary numbers work in a quadratic fashion (x^2) so:
sq(-1) = i
sq(-4) = 2i
sq(-9) = 3i
(so it takes the positive form of the number and square roots it, then multiplies it by i)
Example:
sq(-2) = sq(2)x (i) = (1.4142 x i) = 1.4142i
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What is the square root of minus four?
The square root of -4 is: 2 i
What is 3 root 2 minus root 2?
Oh, what a happy little math problem we have here! When you have 3 times the square root of 2 minus 1 times the square root of 2, you can combine like terms. So, 3 root 2 minus root 2 is equal to 2 times the square root of 2. Just like that, we've created a beautiful, simplified expression.
Simplify 2 minus square root of 5 times 4 plus square root of 5?
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What is the solution to 3 times the square root of 4 minus 2 times the square root of 4?
It is: (3*2)-(2*2) = 2
What is 4 square root of 10 minus the square root of 10?
4 x square root of 10 minus square root of 10 = 3 x square root of 10.
