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How many fourth roots will a positive real number have?
In general, the answer is 4, but only 2 of them are real. For example, the 4th roots of 16 are 2, -2, 2i, and -2i.
What are all the real fourth roots of 256?
The 4th root of 256 is 4
What is the real fourth root of 10 000 over 81?
Restricting to real roots, 4th root of 10000 = +/- 10 4th root of 81 = +/- 3 So 4th root of 10 000 over 81 = +/- 10/3 or +/- 3.33....
Why do square roots come in pairs but cubed roots don't?
The square of a negative number is the same as the square of its positive counterpart, aka its additive inverse ( [-2]2 = 22 = 4), so every positive number has two square roots, a positive one and negative one (both 2 and -2 are square roots of 4). However, the cube of any number will always have the same sign as the original number (23 = 8, [-2]3 = -8). This all follows from simple arithmetic with signs. The product of any two negative numbers is positive, as is the product of any two positive numbers, while the product of a negative number and a positive number is negative. All squares, by definition, are the product of either two positive numbers or two negative numbers, and in either case, the product must be positive. But a cube is the product of a number and its square (x3 = x * x * x = x2 * x). But we already know that the square must be positive, whether original number is positive or negative. So the sign of the original number determines the sign of the cube (because a positive number times a positive number is positive and a positive number times a negative number is negative). If you apply that rule in reverse, then the sign of the cube root must be the same as the sign of the number you are taking the cube root of. Think of it this way. If you are trying to calculate the square root of a number, y, you are looking for another number, x, for which it is true that x * x = y. For any positive number y, there are always two values of x that satisfy that equation, with one being positive and the other being negative, but both having the same absolute value. And therefore, every positive number has two square roots. On the other hand, if you are trying to find the cube root of a number, y, you are looking for a number, z, for which it is true that z * z * z = y. For any number, y, either positive or negative, there will be only one value of z that satisfies that equation. Therefore, every number, positive or negative, has just one cube root. Actually, technically, once you get into higher mathematics, what is really going on is that every number has 3 cube roots, but they all just happen to have the same value. In fact, for any "degree" of root (square root, cube root, 4th root, 5th root, ... 100th root, ...) the number of roots of a number is exactly equal to the degree of the root (a number will have 4 4th roots, 5 5th roots, 10 10th roots, 99 99th roots, etc.) But, if the degree of the root is odd, then all of the roots will have the same value, while if the degree is even, the roots will be evenly split between two values that are the additive inverses of each other. For example, the 5th roots of -243 are -3, -3, -3, -3, and -3, while the 6th roots of 64 are 2, 2, 2, -2, -2, and -2. Note also that negative numbers cannot have any roots of any even degree (square roots, 4th roots, 6th roots, etc.) Actually, even that's not true when you get into really advanced math. Even negative numbers have even-degree roots, it's just that the roots are not real numbers. They are "imaginary" numbers. This is, I'm sure, way beyond your level of education in mathematics, and I'm not trying to confuse you. But if I hadn't included these last two paragraphs, some wise-guy mathematician would come along and "correct" me, and in the process probably confuse you even more. For your purposes, however, just ignore the last two paragraphs.
What is the 4th root of 25?
The 2 real roots are ±2.236 approx.If the domain is extended to complex numbers, there are also ±2.236i where i is the imaginary square root of -1.
Is 10 to the negative 4th power a positive number?
Yes. Any positive number to an exponent is positive.
What is the forth powerof a positive integer?
let x be any positive integer then x4 is the 4th power of that positive integer
How do you factor out x cubed minus 1?
One obvious root of this is x = 1, so (x-1) is a factor. Use long division of (x3 -1)/(x-1) and the quotient (x2 + x + 1) will be another factor. So (x3 -1) = (x-1)(x2 + x + 1). Remember that a cubic polynomial will always have 3 roots. It will either be 1 pure real root and 2 complex roots, or 3 pure real root. In this case (x2 + x + 1) has two complex roots, and cannot be factored with real numbers. In general, any odd-powered polynomial (3rd order, 5th order etc), will have at least one pure real root, and then pairs of either pure-real or complex roots. Any even powered polynomial (2nd order, 4th order, etc) will have pairs of either pure-real, or complex roots. Don't be fooled if you only find one root. Example: (x2 + 2x + 1) actually has a double root, as it is factored into (x+1)(x+1).
What is simplest radical form?
Simplest radical form means simplifying a radical so that there are no more square roots, cube roots, 4th roots and such left to find. It also means removing any radicals in the denominator of a fraction.
What is the 4th episode of Jonas?
keeping it real
What is -2 to the 4th power?
It is 16.2^4 is equal to 16.
Quadrant with x value are positive and y value are negative?
4th quadrant
