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What are the 3 cube roots of -1?
4
What is the cube root of -8 with complex answers?
-21 + 1.7320508i1 - 1.7320508i
How many cube roots does -512 have?
The number -512 has three cube roots in the complex number system. In general, any non-zero complex number has three distinct cube roots. For -512, these roots can be expressed in the form ( r^{1/3} (\cos(\theta/3) + i \sin(\theta/3)) ), where ( r ) is the magnitude and ( \theta ) is the argument of the complex number. The three cube roots are evenly distributed around the unit circle in the complex plane.
How many cube roots does 1 have?
The number 1 has three distinct cube roots in the complex number system. These roots are 1, (-\frac{1}{2} + \frac{\sqrt{3}}{2}i), and (-\frac{1}{2} - \frac{\sqrt{3}}{2}i). In polar form, these roots can be represented as (1), (1 \text{cis} \frac{2\pi}{3}), and (1 \text{cis} \frac{4\pi}{3}), where "cis" is shorthand for (\cos + i\sin).
How do you do cube roots quickly?
Some calculators don't have cube roots, so you could use X to the power of 1/root. x^(1/root). The cube root of 64 equals 4 because 4*4*4 (or 4^3) gives 64. You can reverse these powers by reciprocating the exponent: 64^(1/3) = 4
What are the 3 cube roots of -1?
4
What is the cube root of -8 with complex answers?
-21 + 1.7320508i1 - 1.7320508i
What is the Real cube roots of 0.125?
3√0.125 = 0.5 (there is only 1 real cube root of 0.125).
How do you do cube roots quickly?
Some calculators don't have cube roots, so you could use X to the power of 1/root. x^(1/root). The cube root of 64 equals 4 because 4*4*4 (or 4^3) gives 64. You can reverse these powers by reciprocating the exponent: 64^(1/3) = 4
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 do square roots have two solutions and cube roots only have one solution?
Square roots only have two solutions if the number is positive, if the number is negative it has no solutions.Actually ALL numbers (including negative numbers) have two square roots and three cube roots - just not all of them are real numbers; some are complex numbers.What is a complex number?A complex number is a number which is the sum of two parts: a real part and an imaginary part, ie are of the form (a + bi):a is the real part;bi is the imaginary part which is a real number (b) multiplied by the square root of -1 which is an imaginary value. To avoid having to write √-1 all the time, the little 'i' is used instead, ie i² = -1.Now the square roots of negative numbers can be found:eg √-4 = √(4 × -1) = √4 √-1 = 2i → the square root of -4 is ±2i.What about cube roots?³√8 = 2 is the real root, but there are two further complex roots: (-1 + √3 i) and (-1 - √3 i). I'll cube the first to show it does indeed equal 8 (remember that i² = -1)(-1 + √3 i)³ = (-1 + √3 i)(-1 + √3 i)(-1 + √3 i)= (-1 + √3 i)((-1)×(-1) + -1 × √3 i + -1 × √3 i + (√3 i)×(√3 i))= (-1 + √3 i)(1 - 2 (√3 i) + 3i²)= (-1 + √3 i)(1 - 2 (√3 i) + 3 × -1)= (-1 + √3 i)(1 - 2 (√3 i) - 3)= (-1 + √3 i)(-2 - 2 (√3 i))= (-1 + √3 i)(-1 - √3 i) × 2= ((-1)² - (√3 i)²) × 2= (1 - (-3)) × 2= (1 + 3) × 2= 4 × 2= 8Similar cubing of (-1 - √3 i) equals 8.
What is prime with cube roots?
All numbers have cube roots (not necessarily integral cube roots) so every prime has cube roots.
Who created square roots and cube roots?
The ancients - Egyptians or Greeks. They probably came across the square root of 2 when considering the diagonal of a square with sides of length 1. The cube root of 3 would have arisen, similarly, with the principal diagonal of a unit cube.
Is 2 less than 9 raise to 1 over 3?
Yes.2^3 = 8 < 9 Taking cube roots, 2 < 9^(1/3)
How do you find cube root of 1?
The real cube root of 1 is 1, since 13 = 1. There also a pair of complex cube roots.
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)
Do negative numbers have cube roots cube roots?
Yes.
