It is a root of a number where that root cannot be made into a rational number. For example, the cuberoot(27/64) is 3/4 and so is not a radical but cuberoot(32/64) = cuberoot(1/2) = 3√(1/2) cannot be simplified or rationalised further.
cuberoot(8) + cuberoot(8) + cuberoot(8) = 6
9000
The answer depends on the functions that you may use. A possible solution: cuberoot(8) + cuberoot(8) + cuberoot(8) = 2 + 2 + 2 = 6
It depends on the fraction. Sometimes it helps to convert the decimal into a rational fraction. For example, 0.296296... recurring = 296/999 = 8/27. Now so cuberoot(8/27) = cuberoot(8)/cuberoot(27) = 2/3 = 0.66... recurring. This method only works if the cuberoot is a simple rational fraction. In general, however, the best option is numerical iteration, using the Newton Raphson method. To find the cuberoot of k, let f(x) = x^3 - k. then finding the cuberoot of k is equivalent to finding the 0 of f(x). Let f'(x) = 3*x^2 [the derivative of f(x)] Start with an approximate answer, x(0). Then for n = 0, 1, 2, ... Let x(n+1) = x(n) - f(x(n))/f'(x(n)) The sequence x(0), x(1), x(2), ... will converge to the cuberoot of k. The iteration equation, given above, is much easier to read if the n and n+1 are read as suffices, but the new and "improved" browser cannot handle suffices!
If, by "3 radical 27" you mean the cuberoot of 27, the answer is YES. If you mean 3 times sqrt(27), the answer is NO.
27^(2/3) = [cuberoot(27)]^2 = 3^2 = 9
There is no easy way. For example the cube root of 30 is irrational. Now, because 27 < 30 < 64 then, taking cube roots, 3 < cuberoot(30) < 4. But that is as far as it goes! If the number ends with 000 then the cuberoot is a multiple of 10. So that cuberoot(27000) = 10*cuberoot(27) = 10*3 = 30. But there are many numbers ending with 000 between 27000 and 64000 for which this will not work.
It is a root of a number where that root cannot be made into a rational number. For example, the cuberoot(27/64) is 3/4 and so is not a radical but cuberoot(32/64) = cuberoot(1/2) = 3√(1/2) cannot be simplified or rationalised further.
cuberoot(8) + cuberoot(8) + cuberoot(8) = 6
9000
The answer depends on the functions that you may use. A possible solution: cuberoot(8) + cuberoot(8) + cuberoot(8) = 2 + 2 + 2 = 6
It depends on the fraction. Sometimes it helps to convert the decimal into a rational fraction. For example, 0.296296... recurring = 296/999 = 8/27. Now so cuberoot(8/27) = cuberoot(8)/cuberoot(27) = 2/3 = 0.66... recurring. This method only works if the cuberoot is a simple rational fraction. In general, however, the best option is numerical iteration, using the Newton Raphson method. To find the cuberoot of k, let f(x) = x^3 - k. then finding the cuberoot of k is equivalent to finding the 0 of f(x). Let f'(x) = 3*x^2 [the derivative of f(x)] Start with an approximate answer, x(0). Then for n = 0, 1, 2, ... Let x(n+1) = x(n) - f(x(n))/f'(x(n)) The sequence x(0), x(1), x(2), ... will converge to the cuberoot of k. The iteration equation, given above, is much easier to read if the n and n+1 are read as suffices, but the new and "improved" browser cannot handle suffices!
7
~2.519
They are cuberoot(3) = 1.442 metres (approx)
cube root of 27 = 3, so 3^12 = 531 441 * * * * * If the question is about 27x, rather than 27, the answer is as follows: cuberoot(27x12) = (27x)12/3 = (27x)4 = 531441x4