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One cubic root is -2. The other two are complex numbers - all have the same absolute value, and they are at an angle of 120 from one another. Since -2 = 2 at an angle of 180°, the other two cube roots are 2 at an angle of 60°, and 2 at an angle of -60°. Use your calculator's polar-to-rectangular conversion to separate this into the real and imaginary components, if you want to present the answer that way.
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How do you find the cube root of a negative number?
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√3" and "1-i√3" Therefore the three cube roots of -8 is <"-2", "1+i√3", "1-i√3">
What is the side length of a cube with a volume of 512 cm cubed?
8 cm, just find the cube root of 512
Cube root of -512?
The cube root of -512 is: -8
How do you find the cube root of -8?
Don't know how you find it but I guess the answer is -2. -2 x -2 =4 4 X -2 = -8
How do you calculate the area of the base of a cube?
The base of a cube is a square, so the area of the base of the cube is the area of that square. The area of a square is s2, where s is the length of on side. Side all edges of a cube have the same length, it doesn't matter which edge you use. Example: Find the area of the base of a cube with edges of length 7: A = 72 = 49 Example: Find the area of the base of a cube with volume 8 cubic meters. The volume of a cube is equal to s3, where s is the length of a side. 23=8, so 2 is the length of a side, and the area of the base is 22 = 4.
What are three cube roots of 8?
The cubic root of 8 = 2 2 * 2 * 2 = 8
How do you find the cube of 8?
Cube it. 8^3. Cubed means to the power of three.8x8x8=512
How do you find the cube root of a negative number?
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√3" and "1-i√3" Therefore the three cube roots of -8 is <"-2", "1+i√3", "1-i√3">
Why dont you have three answers for cube root?
You do. The other two are complex numbers, of interest only tomathematicians and engineers, and usually not listed.For example, the three cube roots of 8 are:2-1 + i sqrt(3)-1 - i sqrt(3)
How do you write cubed roots?
In mathematics, a cube root of a number, denoted or x1/3, is a number a such that a3 = x. All real numbers (except zero) have exactly one real cube root and a pair ofcomplex conjugate roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8 is 2, because 23 = 8. All the cube roots of −27iareThe cube root operation is not associative or distributive with addition or subtraction.The cube root operation is associative with exponentiation and distributive with multiplication and division if considering only real numbers, but not always if considering complex numbers, for example:but
What is the cube root of -8 with complex answers?
-21 + 1.7320508i1 - 1.7320508i
What is the definition of a cube root?
The cube root for a real number is the value that when multiplied by itself three times produces that number. So that the cube root of B is A where A x A x A = B.Examplesthe cube root of 8 is 2... (2x2x2=8)the cube root of 27 is 3...(3x3x3=27)The special cases are 0 and 1, which are by definition their own roots (square roots, cube roots, etc.) because all powers of 0 and 1 are still the same value, zero or 1.Perfect cubes are numbers that can be cube-rooted into an integer.These include the numbers 0, 1, 8, 27, and so forth.Negative numbers can also be perfect cubes.-1x-1x-1=-1-2x-2x-2=-8-3x-3x-3=-27For non-perfect cubes, the root includes a repeating decimal requiring rounding.
Find the cube of 8?
8 x 8 x 8 = 512
How is the volume of an 8 inch cube 512?
To find the volume of a cube V = s^3. Therefore a cube with a side of 8 inches is calculated like 8 x 8 x 8 which equals 512.
What are the cube roots of zero plus 8i?
The 3 cube-roots of 8i are:√3 + i-√3 + i-2iThink of 8i in polar form as 8∠90°. A number raised to a power (in this case 1/3) is the magnitude raised to the power and the angle is the angle times the power.So 8 raised to 1/3 power is 2. And 90° * (1/3) = 30°. To find the angles of the other 2 cube-roots, find equivalent angles (add 360° & 720°). So you have 450°/3 = 150° and 810°/3 = 270°.So the three roots: 2∠30°, 2∠150° & 2∠270°. Which are the three answers, above (in rectangular coordinates)
Which part of a cube is a vertex?
A vertex of a cube is its corner points. A cube has 8 vertices and six faces. It also has 12 edges. A cube is a three-dimensional figure.
What are some real world examples of cube roots?
The cubed root of 27 is 3. The cubed root of 8 is 2.
