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2. How do you use Newton's Method to approximate the value of cube...

   socratic.org/questions/how-do-you-use-newton-s-method-to-approximate-the-value...

   Aug 22, 2014. The Newton-Raphson method approximates the roots of a function. So, we need a function whose root is the cube root we're trying to calculate. Let's say we're trying to find the cube root of 3. And let's say that x is the cube root of 3. Therefore, x3 = 3. For the Newton-Raphson method to be able to work its magic, we need to set ...

3. What is the cube root of #(sqrt3 -i)#? - Socratic

   socratic.org/questions/what-is-the-cube-root-of-sqrt3-i

   2 Answers. I would start by converting the number into trigonometric form: z = √3 − i = 2[cos(− π 6) + isin(− π 6)] The cube root of this number can be written as: z1 3. Now with this in mind I use the formula for the nth power of a complex number in trigonometric form: zn = rn[cos(nθ) +isin(nθ)] giving:

4. How do I rationalize Cubic root? + Example - Socratic

   socratic.org/questions/how-do-i-rationalize-cubic-root

   Example 1. Rationalize the denominator: 2 3√5. We'll use the facts mentioned above to write: 2 3√5 = 2 3√5 ⋅ 3√52 3√52 = 2 3√25 3√53 = 2 3√25 5. Example 2. Rationalize the denominator: 7 3√4 . We could multiply by 3√42 3√42, but 3√16 is reducible! We'll take a more direct path to the solution if we Realize that what we ...

5. How do you write x^(2/3) in radical form? - Socratic

   socratic.org/questions/how-do-you-write-x-2-3-in-radical-form

   Explanation: First, we can rewrite the term as: x2× 1 3. Next, we can use this rule of exponents to rewrite the term again: xa×b = (xa)b. x2× 1 3 ⇒ (x2)1 3. Now, we can use this rule to write the term as an radical: x1 n = n√x. (x2)1 3 = 3√(x2)

6. How do you find three cube roots of 1+i? - Socratic

   socratic.org/questions/how-do-you-find-three-cube-roots-of-1-i

   As we are going to find cube roots, what we seek is (1 + i)1 3. For that let us first write 1 + i in polar form. As 1 +i = 1 +1i, r = √12 + 12 = √2 and θ = tan−1(1 1) = π 4. Hence 1 + i = √2(cos(π 4) + isin(π 4)) and therefore 3√1 + i = (√2)1 3⎛ ⎜⎝cos⎛ ⎜⎝ 2nπ +(π 4) 3 ⎞ ⎟⎠ + isin⎛ ⎜⎝ 2nπ+ (π 4) 3 ...

7. How do I find the cube root of a complex number? - Socratic

   socratic.org/questions/how-do-i-find-the-cube-root-of-a-complex-number

   To find a cubic root (or generally root of degree n) you have to use de'Moivre's formula: z1 n = |z|1 n ⋅ (cos(ϕ+ 2kπ n) + isin(ϕ + 2kπ n)) for k ∈ {0,1,2,...,n −1} From tis formula you can see, that every complex number has n roots of degree n. So to calculate root of a complex number you first have to write the number in a ...

8. What is the cubed root of the square root of 64x^3? - Socratic

   socratic.org/questions/what-is-the-cubed-root-of-the-square-root-of-64x-3

   Explanation: (√64x3)1 3 = (26 ⋅ x3)1 6. = 2 ⋅ x3 6. = 2 √x. Answer link.

9. How do you find the cube roots #root3(27)#? - Socratic

   socratic.org/questions/how-do-you-find-the-cube-roots-root3-27

   3 It is helpful to know the first 5 cube numbers. 1^3=1;" "2^3=8;" "3^3=27;" "4^3=64;" "5^3=125 root(3)27" " is the number cubed that gives " " 27 from the list is seen that it is " "3

10. How do you find the domain of #g(x) = root3(x+3)#? - Socratic

    socratic.org/questions/how-do-you-find-the-domain-of-g-x-root3-x-3

    Explanation: We have a cube root here, Note that while even powers are all positive, odd powers can be negative as well. Therefore whether x +3 is positive or negative, we can find its cube root. Hence, domain of g(x) = 3√x +3 is x:x ∈ R and x ∈ (− ∞,∞) Answer link. The domain is RR. See explanation. To find the domain of a function ...

11. Find cube root of 15 by using iteration method? - Socratic

    socratic.org/questions/find-cube-root-of-15-by-using-iteration-method

    cube root of 15 correct to three decimal places is x=2.466 Let the cube root of 15 be x Then, cubing both sides and interchanging x^3=15 x^3-15=0 Let f(x)=x^3-15 We need to investigate for the roots of the polynomial x^3-15 Consider any perfect cube close to the number 15 1^3=1,,,,,,,2^3=8,,,,,,,,,,, 3^3=27 15 lies between 8 and 27 Hence cube root of 15 lies between 2 and 3 Let us guess the ...