Students should also take away that math teachers sometimesĬube root of a number is just the same as raising to the power 1/3. Is it Real to Real Real to Complex Complex to Real or Part of problem is fuzzy statement of domain and range The user has to do quite a bit of thinking to extract the complete answer from it.Ħ Comments on “Is cube root the same as raising to power 1/3?” I find it strange that Wolfram|Alpha gives only a partial graphical answer for the cube root of −8.
0.3 times 10 to the first power full#
It's doing its best to figure out what you want to know, but can't be expected to know the full context of your query, or necessarily give you all the possible answers. Conclusionĭon't just accept the computer's word for it when it gives you a graph, or the solution for some equation. Wolfram|Alpha and Scientific Notebook recognise there is a difference between (there is one "principal" answer each time) and, where we need to remember the complex roots. The answer there is one solution of course, whereas if you are asked to solve, you will get 2 solutions. I've written before about the number of solutions for √16. Geogebra and Desmos answersīoth Geogebra and Desmos give the same "full real value" graph for both and.
The blue graph is, and Scientific Notebook gives the full real solution (in first and third quadrants), while the magenta (pink) graph, is in the positive quadrant only. Here's what Wolfram|Alpha returns when I ask it to graph : So we would expect the graph for to be the same as the one for. We learn early in the study of roots and fractional powers that we can write roots in terms of fractional exponents. There is an option to see the "principal root", but this just gave the same result. NOTE: In tiny font, Wolfram|Alpha states:Īssuming "cube root of" is the real-valued root. Wolfram|Alpha states there is one root ( x = 0), and the domain and range are all real numbers, which is consistent with the graph above. We know that that cube root of a negative number is negative, so for example, and we can see this makes sense on the graph above. This graph is the reflection of the graph y = x 3 in the line y = x. In the search box, I put "cube root of x", and it stated the "Result" was correctly written as.
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