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Because there is no real number which you can square, which will result in a negative real number. So they came up with imaginary numbers, and denoted the letter i to represent the square root of negative one. At first, they were thought to be just that - imaginary - nonexistent, whose only purpose was to fill in and make equations solvable. But now these numbers are useful in solving equations which govern electrical waves and other types of wave motion.

Q: Why is the square root of a negative number not a real number?

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The square root of any negative number is not even a 'real' number. It's called 'imaginary', because there's no number you can multiply by itself to get a negative number. The square root of 101 is irrational.

no, every number is a real number --- There are numbers that are not real numbers. They are called imaginary numbers, and have the property that when they are squared, the result is negative. The square root of -1 is called i, and the square root of any other negative number is i times the square root of the absolute value of the number. So the square root of -4 is 2i.

The square root of negative 64 isn't even a real number. In math and engineering, it's called an "imaginary number".

An imaginary number such as the square root of any negative number.

The square root of a negative real number is an imaginary number.We know square root is defined only for positive numbers.For example,1) Find the square root of (-1)It is imaginary. We say that square root of (-1) is i.In fact they are not real numbers.2) Find the square root of (-4)-4 can be written as (-1)(4)Square root of 4 is 2 and square root of (-1) is iSo, the square root of -4 is 2i.Similarly, we can find the square root of other negative numbers also.Source: www.icoachmath.comAn imaginary number is defined to handle square roots of negative numbers. The imaginary unit i is defined as the 'positive' square root of -1.

Related questions

The square root of a negative number is not real.

No. In general, the square root of a negative number is an imaginary number, which is not a real number.

No, it is not, because real numbers include negative numbers. The square root of a negative number is an imaginary number

There is no real number [square] root of a negative number. There is a real cube root and a real fiftth root etc, but root, by itself, implies square root.

Neither. All irrational numbers are real numbers.Using the real number system you can't take the square root of a negative number, but if you're dealing with imaginary numbers then the square root of negative 3 is the square root of 3i

Imaginary number

Yes. In general, the square root of any non-negative number is a real 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 .

No, it is not even a real number. The square root of negative 5 is the square root of 5, times i.

Nothing. You cannot have a square root of a negative number. The square root of negative one is called i, but i is an imaginary number. It does not exist and does not follow the properties of real numbers. (For example, if a and b are positive, then the square root of a times the square root of b is the square root of ab. But the square root of -7 is not the square root of 7 times i.)

The square root of 100 is rational since it is not repeating.

Actually the square root of 180 is 13.416407864998738178455