Algebra

# Is the cube root of negative number a positive?

012 ###### 2017-03-03 15:51:46

No.

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0 ###### 2013-10-23 08:39:35

No, because the inverse function would not work. Every time you multiply a positive by a positive you get a positive.

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## Related Questions   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 .  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 &radic;4 = +/- 2 &radic;(-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&radic;8 = 2 3&radic;(-8) = -2 Every positive integer has two square roots, a positive square root and a negative square root. This is because, just like a positive number multiplied by a positive number is equal to a positive number, a negative number multiplied by a negative number is equal to a positive number. Therefore, rounded to two decimal places, the positive square root is equal to 7.28, and the negative square root is -7.28. Because if you multiply a negative number three times, the product will be negative. yes, you can find a real root to the cube root of any negative real number. There will also be two complex roots which satisfy it, as well. I am pretty sure that the cube root of negative seven is a surd. I checked on the calculator.......and it showed a negative number.....??I think when it is not a surd...it's supposed to say error, so the number probably means that it is a surd.. Negative 2 (times) cube root of 54 = -7.55953 Negative 2 (plus) cube root of 54 = 1.77976 The square root of a real number is not always positive. The square root of any positive number is positive, the square root of zero is zero (not positive), and the square root of a negative number is complex (i.e. neither positive nor negative). The square root of 16 = -4 or 4. The square root of 0 = 0 The square root of -16 = -4i or 4i If the negative number is "-a", then you can say the cube root is "-(cube root of a)" Because if you cube a negative number, you get a negative number. So if you cube root a negative number, you get a negative number. Ex) cube root of -8 = -2 Because (-2)^3 = -8 But if you want to find the complex cube roots, you can make an equation: "x^3=-a" or "x^3+a=0" We know one of the roots is "-(cube root of a)" so you can factor the equation by (x+(cube root of a)) And then you use the quadratic formula for the quadratic equation you're left with. Ex) x^3=-8 or x^3+8=0 Since -2 is a root, factor it by (x+2) x^3+8=(x+2)(x^2-2x+4) Using the quadratic formula, you get "1+i&radic;3" and "1-i&radic;3" Therefore the three cube roots of -8 is &lt;"-2", "1+i&radic;3", "1-i&radic;3"&gt; If "a" is positive, it will have two fourth roots, one will be positive and one will be negative it will have one fifth root, which will be positive. If "a" is negative, it will have one fourth root, which will be negative. it will have one fifth root, which will be negative. A positive number has two square roots, its principal (positive) root and its negative root. This is because a negative number multiplied by a negative number equals a positive number. In this instance, the square roots of 256 are 16 and -16. using basic math principles, you can't find the square root of a negative number because in order for a number to be a square root, you have to multiply it by itself to get your radical. since a negative times a negative and a positive times a positive are both positive, it is impossible to find the square root of a negative number Every number has two square roots ... a positive one and a negative one. Example: +2 and -2 are both square roots of 4, because when you multiply either of them by itself, the answer is 4. The positive square root of a number is the square root that's not negative. The non-negative square root of a number is the positive one. Any real number - positive or negative - has exactly one real cube root. Any real number (except zero) has three cubic roots in the complex numbers; but only one of them is real. Because negative numbers multiplied by themselves three times will be negative. Yes as for example the cube root of -27 is -3 I think it is Xi (whatever the square root of the positive is times i). i is an imaginary number that when you square it, it becomes negative. eg. the square root of -4 is 2i. Without "i", it would be impossible to square root a negative number, as any number times itself will always equal a positive. 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. 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. The answer is an imaginary number, because of the negative under the square root. The same number multiplied together will always be a positive number. For example, if you square negative one, the answer is positive one, because a negative times a negative is a positive. Because a square root undoes a square, there is no solution to the square root of a negative number. That's why your calculator could not compute this problem. However, there is a way to solve these types of problems by using imaginary numbers. The answer is 13i, where i is the square root of negative one. Definition of Square Root: The Square Root of a number 'X' is equal to 'A' when X=A*A By definition, the square root of a positive number has two answers, one negative and one positive, that have equal magnitudes. i.e. The square roots of 4 are 2 and -2. The Non-Negative Square Root is simply asking for the positive root. The product of two negative numbers is a positive number. Ergo, the product of the square of a number is equal to the square of its negative equivalent.

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