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Why can you cube root a negative number but you cannot square root a negative number?
Wiki User
∙ 7y ago
When two negative or two positive numbers are multiplied together, they always result in a positive number; and when a positive and a negative number are multiplied together, they will always result in a negative number. Thus, you cannot square root a negative number because there are no real numbers that, when squared, would result in a negative number.
For example:
(-2)(-2) = 4
(2)(2) = 4
√4 = +/- 2
√(-4) = ? No real number, when squared, is a negative! Does not exist!
The cube of a number is different, because you are multiplying three numbers together instead of just two. As a result, you can get a negative or a positive number.
For example:
(-2)(-2)(-2) = -8r
(2)(2)(2) = 8
3√8 = 2
3√(-8) = -2
Wiki User
∙ 7y ago
Wiki User
∙ 7y agoYou can, only not in elementary mathematics.
The simple reason is that the cube of a negative number is negative, whereas a cube of any number is non-negative. (It is positive apart from the square of 0).
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Is the cube root of a negative number positive or negative?
The cube root of a negative number is negative
Why isn't it possible to take the square root of a negative number while you can find the cube root?
think about it this way... a negative times a negative is a positive... squaring is the same as multiplying it by itself. 4^2 is 16, 4X4 is 16. -7X-7 is positive 49. So a square can't be negative, therefore a negative cannot be square rooted.
What is a number which is a square and a cube?
Square=2 Cube=3
How do you find the cube of a negative number?
The cube of a negative number is negative. Negative times negative is positive, but then you have the third multiplication, and positive times negative is negative. So for example (-2)3 = -8.
What is the real number root of -25?
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.
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 .
Is the cube root of a negative number positive or negative?
The cube root of a negative number is negative
Is 196 perfect square or perfect cube?
196's prime numbers are (2) (2) (7) (7). For example, if you square those prime numbers you would get 14. Why? Because u need equal integers within a square root, so that you can take that integer outside the square root. With the same knowledge, we can apply ask the question whether 196 is a cube root. If it's a cube root, then it needs to have 3 same integer (ex: 3x3x3x4x4x4x; 2x2x2x7x7x7). As you can see we don't have third same integer. Also, even if it is 2x2x2x7x7, it cannot be a cube root because it is missing the third 7. So the answer is that 196 is a perfect square and not a perfect cube. Note: you cannot have a square root of a negative integer, if the question is "is -196 a perfect square or a perfect cube", then the answer is neither. Of course you can SQUARE the negative number (ex: (-2)^2=+/- 4), but you cannot mathematically square root a negative number unless your using the imaginary integer "i". I hope it answers your question and just a bit more.
Why isn't it possible to take the square root of a negative number while you can find the cube root?
think about it this way... a negative times a negative is a positive... squaring is the same as multiplying it by itself. 4^2 is 16, 4X4 is 16. -7X-7 is positive 49. So a square can't be negative, therefore a negative cannot be square rooted.
Can you find the cube root of a negative number If so is it positive or negative?
The cube root of a negative number is negative.
What is the probability of rolling a negative number on a number cube?
It depend how many negative numbers are written on the cube.
What is a number which is a square and a cube?
Square=2 Cube=3
Is the cube of a number bigger than the square of a number?
-- If the number is more than ' 1 ', then yes. -- If the number is ' 1 ' or less, including negative numbers, then no.
Program to find square and cube of a number?
square and cube caculator
What number is both a square number and a cube number between 1 and 25?
There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.
How do you find the cube of a negative number?
The cube of a negative number is negative. Negative times negative is positive, but then you have the third multiplication, and positive times negative is negative. So for example (-2)3 = -8.
What is the real number root of -25?
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.
